Summer signing Raya made his Gunners debut in their 1-0 win at Everton yesterday.
Ramsdale has been No1 since joining from Sheffield United for £30million last year, but Mikel Arteta had made it clear there is no guaranteed first-choice.
Odegaard believes Arsenal are "lucky" to have such strength in depth in goal and has backed Ramsdale to respond to the new competition.
"I think he will just keep working hard, like he is always doing," he said. "Today he was there supporting us, cheering for us, helping us. He is a great character and he showed a very good response today by backing the team. It was excellent from him.
"We have two good goalkeepers and big competition. They have different qualities. They are both so good on the ball and in goal as well. So, we are lucky to have two such good goalkeepers and we will see who plays."
Arteta defended his decision to drop Ramsdale, explaining how he views the goalkeeping position like an outfield one.
The Arsenal boss revealed that twice during his managerial career he had regretted not substituting a goalkeeper during a match, and his words pointed towards a scenario where Ramsdale and Raya will be rotated.
"I haven't had a single question on why Gabriel Jesus hasn't started," said Arteta. "He's won more trophies than anyone, including me, in that dressing room. It's something that has been historically done like this, but I cannot have two players like this in one position and not play them. No one is guaranteed a spot.
"We're here to perform at the highest level and to contribute at our best capacity to win games. It's no different for anybody."
Raya marked his debut with a clean sheet, but had very little to do during a game Arsenal dominated.