what would stop some players from moving to another club would be their weekly wages, even if they wish to leave the club that they are, they won't still want to leave because if they do, their weekly due would reduce and it pays them to stay at their present club, finish the contract with them and become free agent. Raheem Sterling want to leave Manchester City because he didn't have playing time, he's always on bench, his appearance in the season that just ended isn't much, there are many players that can play his position, even Jack Grealish that recently come is always on bench.
Raheem Sterling leaving isn't the problem, the problem is the amount that he's collecting, he is collecting 300k every week at Manchester City. Chelsea has been eyeing him, Thomas Tuchel is a big fan of him, so he would definitely be happy if he finally land to Chelsea and of course he would have playing time that he is looking for at Chelsea since a fan of him is the coach and of course Guardiola don't hold players, he can't stop those that are not happy to stay, they need playing time and they can find in in another club, Gabriel Jesus would play until he would have fatigue at Arsenal, he would find the playing time he want.
Would Chelsea be able to pay more than 300k pounds every week? I said more than because whenever a player is moving, he would definitely demand for additional money, the money that is higher than the amount he's collecting as the club that he is moving from. Gabriel Jesus is collecting double amount of money Manchester City are paying him as he reach Arsenal. If Chelsea give Raheem Sterling 300k weekly, he would be the highest paid because Ngolo Kanté is Currently the highest paid player in Chelsea, he's collecting 290k every week.
Almost all players that their country qualified for World Cup are finding all means to have playing time so they can participate in the World Cup, maybe Raheem Sterling would collect pay cut and play at Chelsea if he really want to have have playing time towards the upcoming World Cup. There are too much competition at Manchester City so he can't have time to prove himself, it's better for him to wise up, not to sign long term contract for Chelsea if he would move to the club so after World Cup, he should find another club.