Out of those three, the one I'd keep would be Mahrez.
Jesus was a good player, and worked hard. However, he wasn't quite at the level that we need unfortunately. I do think he will do well at Arsenal and they will love him as he will put in a shift and score plenty of goals. It sounds maybe a but much, but I think he will thrive at Arsenal as he will find his level. That's not to say he's a bad player, far from it, but there's a world of difference between playing at Arsenal and City. He's had plenty of time to kick on and make the striker shirt his own, but he's not quite good enough - despite the odd world class performance.
As for Sterling, his movement is world class and his pace and trickery will terrify any defence. However, when it comes to it, if he has to think then we all know where the shot it going - straight into some kids face sat to the left/right of the goal. If he could finish, he would be right up there as one of the very best in the world. As he starts getting past 30, when his pace slows, what kind of a player will he become? Luckily, I don't have to care about that but Chelsea will do.
The reason I'd keep Mahrez is that I think he's probably got the best touch of a player I've ever seen. He just never miscontrols the ball, no matter how bad the pass is. I think he has all the ability in the world - he can go past defenders with his trickery, but doesn't rely on pace. He can more than find a pass too and is capable of world class passes, shots and dribbles. He's scored some big goals for us too, especially in the CL. He's rarely injured either. Whilst he's not slow, his football brain means he is likely to be able to play well into his 30s as well.
The club have got it completely right on this.