This is according to Spanish football expert Guillem Balague, who tweeted the news to his 844,000 followers on Monday afternoon after reports emerged that Arsenal are in talks with the 24-year-old's agent.
Balague claims Gabriel - who joined Villarreal from Brazilian side Vitoria in 2013 - is on the radar of Manchester United manager Louis van Gaal. It's believed the Dutch coach has also submitted a €35 million offer for Valencia centre-back Nicolás Otamendi - but that bid has been rejected.
Gabriel's reputation on the rise
Gabriel Paulista will not be a name familiar with too many Manchester United fans, but the South American has cemented his status as arguably Villarreal's most important defender this season.
The Yellow Submarine has not lost a match in any competition since their 3-2 defeat to FC Zurich in the Europa League on November 6 - a run which now stretches 15 games - and Gabriel has played an instrumental role in the club's superb purple patch.
Van Gaal has doubts over United's centre-backs
An ever-present this season, Van Gaal may regard Gabriel as a reliable alternative to any of his first-choice centre-backs, all of whom have suffered with various injury problems this season.
It's believed Van Gaal has doubts over Chris Smalling, Phil Jones and Jonny Evans; while the likes of Paddy McNair and Tyler Blackett have coped admirably after being thrown into the deep end this season but doubts persist over their quality.
Van Gaal insists that little business will occur at Old Trafford between now and when the January transfer window closes in two weeks' time - but it appears he has his sights set on signing at least one quality centre-back.
Manchester United's defensive frailties
Manchester United, despite the fact they have conceded fewer Premier League goals than champions Manchester City, have looked defensively vulnerable at times this season and are in need of a defensive leader.
But the Red Devils faithful are expecting a proven defender with considerable experience under his belt to arrive at Old Trafford - such as Borussia Dortmund captain Mats Hummels - and may have concerns that Gabriel is no better than any of Manchester United's current centre-back options.
Van Gaal said last week that he would only sign players this month if they're an upgrade on what he already has in his squad - but it seems, at least in the eyes of the United manager, Gabriel may fall into that category of player.