This should be a no-go. Barkley is too similar to Pogba from a functional perspective (except technically weaker and not as good at a lot of other things), and I don't see him thriving with Paul - just like Gerrard and Ballack didn't thrive with Lampard unless they made significant adjustments to their games - which would be counterproductive because Barkley isn't a special enough player to risk a proven template (Pogba + def. box-to-box + holder). Everton will demand top money for him even with his contract situation, and I'd rather United go the extra mile and sign a proper box-to-box with world class potential - like Saúl (who reportedly has a buyout clause of ~£60 million and would be a brilliant foil for Pogba).
Even if you're looking for players with Barkley's profile (tall and strong offensive minded midfielders), United would do well to sign someone like Leon Goretzka instead. More adaptable, likely cheaper because he plays in the Bundesliga and won't be subject to the Premier League premium, a better player right now, and most importantly - he's evidencing quality growth in terms of his tactical awareness and understanding of the game (which bodes well for Goretzka's future and has been a persistent issue with Barkley - all the physical traits in the world but you have to wonder if he just doesn't
get it because he takes one step forward, then one step backwards). Could do with another season at Schalke to mature fully and refine his decision-making, but he'll be on a Bosman in 2018:
Contract until:
30.06.2018
http://www.transfermarkt.com/leon-goretzka/profil/spieler/153084
And the competition for his signature after the World Cup
could be fierce. So he'd make sense on a decent fee in the summer.