I can't see Real Madrid going after him as there's no holes to fill there and it doesn't seem likely there will be any, they've purchased Aurelien Tchouameni they also have Eduardo Camavinga and Federico Valverde all great and young enough players capable of being energetic runners or playing deeper or roaming forward, honestly I think it's more likely they go for proper ball playing midfielders as they still have Casemiro in the middle too he's going nowhere, they'll need great passers of the ball to replace both Luka Modric and Toni Kroos or at least an heir apparent to Modric and whatever we think of Bellingham he isn't exactly a playmaker.
Not impossible by any means but they've already got the makings of a fast energetic team in midfield without him so hopefully Bellingham is far from their thoughts next summer I don't think it makes the slightest bit of sense for them, just think they'll need extra creativity in the next couple midfield signings to go with the ageing Modric and Kroos you've got Isco just leaving them plus they'd be open to selling Asensio too, knowing some of their better creators or subs are ageing or haven't developed exactly how they wanted it seems logical they'll want a creator type really, plus maybe they'll get a defender or two for depth they could certainly do better than Carvajal or at least keep him on his toes letting Hakimi go a couple years back was a big mistake by them.
I think it'll be us or the dippers if they're brave enough to spend £100m and possibly the rent boys too that'll be serious about signing him depending if they move on any midfielders, but I seriously can't see any foreign teams being able to afford Jude except for Real and he might not be what they're looking for if you think about their current squad and what they need long term