Seems like Leicester would make the most sense. Mahrez is presumably leaving and they need creativity and long-passing and shooting between their solid CMs (Ndidi, Iborra, Silva) and their good finishers up top (Vardy, Iheanacho) but Gray and Albrighton are just decent width. They need at least one very creative type and maybe Shaqiri can peak as a sort of middle-class Payet type.
As for him coming here, I think it only makes sense as backup RW if Mata and Martial leave and we do sign Bale or another RW, but I'm not sure Shaqiri is mature enough to be a squad guy.
-----------Lukaku(Rashford)---------
Sanchez(Lingard)------Bale(Shaqiri)
makes sense, and while people might want another star for rotation I do think Rashford has the goods to get there. But we have a creative, left-footed #10/RW who doesn't have great pace in Mata and he seems to not complain about being first choice and while Shaqiri should be entering his prime and Mata leaving his, Mata is still better at the moment.