
But despite being brought up in a loving, close-knit family, she blithely dismisses suggestions she's unhappy being single.
'Motherhood has never been an ambition,' she says. 'I've never had expectations such as: "When I'm 19 I'm going to do this and by the time I've hit 25 I'm going to do that." I take things as they come, each day at a time, and if things happen, all well and good. I just want to be independent and be able to take care of myself. Anything else is just gravy.'
Indeed, Renee isn't one to whinge, insisting she's very happy with her laid-back life. She enjoys her own company, de-stresses with yoga, plays the guitar and loves her job.
'Work has, quite a few times, got me through hard times because it shows up and just keeps on going,' she admits.
But it's hard not to think how much she would enjoy marriage and motherhood. And after digging deeper, it's obvious the actress who found fame in the 1996 film Jerry Maguire does wish for something more meaningful in her life than work - however well regarded she is.
In fact, in a candid moment Renee has admitted that, with the example of her parents, it's difficult for her not to believe in the institution of marriage.
'I've seen it work - who wouldn't want that?' she says.
'Biologically, I look forward to being a cornerstone of a family. I'll be in my glory when I have a child on my knee.'
Renee has also admitted to feeling unsettled when she's at home alone in her $1.6 million mansion in the Connecticut woodland. In fact, when she's not working, she prefers to stay with friends, who are like her extended family.
'It's scary if there's a car idling outside your house in the middle of the woods at four in the morning,' she says.
'As a girl, your instincts are to be scared and that doesn't make for a very good night's sleep. Your instincts kick in, your adrenalin rushes and you realise you can't live there. I don't own a gun but sometimes at four in the morning you do think about it.'
Still, Renee's always an optimist and doesn't stress about the lack of men in her life. And perhaps one of the reasons she's eager not to fret about her love-life is she knows she could easily be painted as a real-life Bridget Jones, having starred in two film adaptations of author Helen Fielding's novels about a woman longing for love.
Renee filled - and filled out for - the role so successfully that for a time it became quite hard to separate the Texan actress from her on-screen persona. But the speed with which she shed the more than 12kg she gained for both roles seemed to underline her eagerness to be different from Bridget.
Yet, physique aside, the similarities between the actress and her character are closer than she might wish to admit. Both have a ribald sense of humour and a history of choosing unsuitable men. And Renee, who turns 40 next year, is still yet to find her prince, despite kissing a fair amount of toads along the way.
In 1992 she had a relationship with Sims Ellis, a musician who committed suicide in 1995. She then dated actor Rory Cochrane, followed by director Josh Pate.
Her most high-profile love affair was with comic actor Jim Carrey, who she met on the set of Me, Myself & Irene. There was even speculation of an engagement, despite the fact the couple had only been dating for a few months at the time. The relationship lasted less than a year, falling apart in 2000 after Renee moved to England to begin work on Bridget Jones's Diary.
Next up was a relationship with The White Stripes frontman Jack White, who is six years her junior. Within a few weeks of its demise, amid rumours she was ready to have children and he wasn't, she met country singer Kenny Chesney at a 2005 relief fundraiser for the Boxing Day tsunami - he was performing while she was manning the phones.
'It's a beautiful thing to find the right person,' she gushed.
By May they were married and Kenny declared himself: 'The luckiest man alive.'
Just four months later, Renee filed for an annulment of the marriage on the grounds of 'fraud'. This legal term implies a form of misrepresentation by one partner to the other, and again it was suggested that while Renee was ready to settle down and begin a family, her younger husband had found the whole relationship scene a bit, well, too heavy for his liking.
It wasn't that Renee didn't try to make it work, with the actress going on tour with Kenny straight after their surprise wedding, cheering him on from the sidelines. But not long after she went alone to pick up her star on the Hollywood Walk of Fame and to the premiere of Cinderella Man.
Renee refuses to talk about the relationship, but denies she has said it was 'the worst mistake' of her life. She insists she'd never utter such a 'hurtful' statement.
'Not everything works out like you hope and I'm not the first person to have disappointment in my life,' she says.
'The only thing I'd ever say about my marriage is: "I carry that time in my heart and I want to keep it there."'
And although she's constantly linked to her Leatherheads co-star George Clooney, Renee insists they're just friends, and have been for the past decade.
Considering the turmoil in her private life, it's no surprise Renee looks to work, family and friends for solace and sanctuary.
Her family - her mother and father and brother Andrew - is particularly important to her, with Renee always considering what impact any role she's offered will have on them. This respect is the reason why she won't take on any risque parts.
'I don't want the first shot of the film to be a close-up of my naked breast because what that leads to doesn't have a place in my life,' she says. '"Drew, Dad, Mum, there's a premiere tonight, you want to come?" I have to keep that in mind.'
Her tumultuous love-life is also the reason Renee says that, for the time being at least, she's happy to stay single and just embrace what she does have in her life.
'I don't want to sound cavalier by saying I'm OK with my situation because I'm not a frivolous person and I wouldn't take on something of such significance lightly,' she says. 'But there's good in every situation. It sounds simplistic, but I still have the good things that have always been in my life.'
By Jane Warren