As far as I know, Barcelona is already interested in him since the last season. But Man City keeps Bernardo Silva, he is an important player for the squad. He still performed well in the last season, no reason to let him leaving. Besides Barcelona may have no money to sign him, Man City seems refuse any offer for Bernardo Silva because he is still a part of Man City plan for the next season.
I don't know what's going on with the player's contract and when it expires, but there were rumours that he might go to Saudi Arabia, he's negotiating and so on. I don't really believe it, of course, because at Manchester City he shows himself very well, but I have a feeling that the right to choose is left to the player himself. Moreover, the reason why the club is not interested in selling the player is that they don't need money, they are doing well, their "business" is perfect