Cole and Daniel Sturridge last night became the second and third current players to speak publicly about a potential move at the club's latest 'An Audience With...' event at Stamford Bridge.
Cole said: "We have to trust Roman. He has put something like £800million in and if you see the training ground and what he has done there - if you look at the bigger picture - you have to trust him."
He added: "Of course people are going to miss Stamford Bridge but, if we want to evolve, I think it is a good move."
Sturridge said: "We do maybe need a bigger stadium because if you look at the biggest clubs in the Premier League and around the world, their stadiums are a bit bigger than Stamford Bridge.
"There is a lot of history at this stadium and fans have been coming here since before I was born, and I am not the person to say I think you should move away. The fans have a right to their opinion."