The defender has impressed on the south coast, having joined last summer, and Brighton are keen to extend their agreement with both the player and Chelsea.
The Blues, however, rate Colwill very highly and incoming manager Mauricio Pochettino will be allowed to decide on Colwill's future once his appointment has been confirmed. Pochettino has a very successful history of working with young players.
Colwill currently faces competition from the likes of Wesley Fofana, Benoit Badiashile, Thiago Silva and Kalidou Koulibaly at Chelsea, though the latter two face uncertain futures.
When asked about Colwill’s long-term future at Brighton, De Zerbi told reporters on Friday: "I would like to work with him for another two, three, four years.
"It’s difficult to find a another centre-back, left centre-back, with his quality.
"He’s a good guy, I think he’s improving a lot. This year his improvement has been fantastic. I hope he can stay with us."