Trott left the England tour of Australia suffering from a stress-related illness at the end of the first Test in Brisbane. But while Cook was keen not to place any timeframe on Trott's return, he did make it clear that he would be welcomed back once he was fully rested and recovered.
"We all understand he's got a long journey back," Cook said. "But I don't see any reason why he couldn't play for England again.
"If he comes back for Warwickshire and scores a lot of runs, we would love to have him back. He's a class player. We've all seen it. But it's important that we give him a little bit of time and space away from the pressure of playing international cricket.
"We'd love to have him back but he's got to make sure he's ready and let's not put any time pressure on him. We all wish him all the luck in the world."
Cook admitted that Trott had experienced stress-related problems in the past and praised his courage in dealing with them over the course of a successful career.
"It's horrible seeing what he's gone through on the last couple of weeks on this tour," Cook said. "Throughout his career, he has struggled at certain times. He's shown a huge amount of character to perform as he has done for England in 49 Tests. He has been outstanding for us at number three.
"I haven't had to fight the same kind of stuff as Trotty, so I appreciate I'm lucky in that sense. It can get tough: that's why it's called Test cricket. There's a lot of tough moments. I've been lucky that I've at certain times found a score, which has relieved the pressure on my place.
"It is important to have a sense of reality. Seeing what Trotty has gone through has given people a bit of that. You realise that it was a tough defeat in Brisbane but someone else is having it a lot worse than we were having it."