Arteta earlier confirmed that they would be buying a striker in next transfer window and some strong sources also confirmed Jesus interest but there should be lot of targets in that list. Not necessary that they would buy him for sure but Jesus is being considered as one of the targets. On plus side, Jesus is a great striker with Premier League experience and has good movement and striker of the ball too so anyone can see why he is being considered as one of the targets. As for other clubs, there will always be competition for the player but eventually the player has to decide and working with Arteta at one point might add up to the chances but well let's see how it goes.
Mbappe to Liverpool or other PL clubs...hmm I am sure that would make massive headlines. Playing for the club as great as Liverpool is a dream but it's about player. We can just speculate what's players dreams are by their idol and so we link him upto Madrid, that's different that eventually his move to Madrid is much more likely. But if speculations come out wrong , then to Liverpool? Why not ..very much possible. If we set those dreams of Mbappe aside and if Mbappe likes how they think of working with him then why not.
Also there were lot of high profile transfers that was hijacked in matter of hours. Take Ronaldo to United for example, Many strong sources were claiming Ronaldo to City but in his matter of hours that deal was hijacked by United. So everything is possible although chances would be slim.