I could see Arsenal making a bid for him, he seems like their type of player, and with him being young English (they have a lot of foreign players) and highly rated (at some point), a possession based team like them would feel they could get the best of them.
They need some big money signings this summer to appease fans, and are being linked with some big money moves, but also know they have no champions league football this year, so will be a blow to attracting the really big names.
Also Barkley has had some of his best performances against them, which always leaves a mark.
The fact we have been linked with a few of their squad players as well (Chambers, Giroud, Gibbs, Perez) could see any of them used as potential bargaining chips.
Just an opinion like, I have no Insider knowledge.