Bertrand would benefit if Cole left the club.
But he told the London Evening Standard: "Yes, I want Ashley to stay.
"He has been a fantastic servant for the club and he rightly deserves what he is asking for. It doesn't affect me and my game [if he stays] because I am getting plenty of chances to play.
"I have learnt a lot from him and the longer he stays the more I will continue to learn. I probably could have a bit of banter with him about me taking his place in the team because we have a really good relationship but we're more than happy playing together and to leave it as it is."