The midfielder is also a target for Arsenal and Tottenham Hotspur, according to the Daily Express.
However, the Red Devils seem most likely to sign the 25-year-old, and could do so very soon. The Saints are keen to wrap up the midfielder’s future before they go on their pre-season tour of Austria and Holland, which they start with a game against RasenBallsport Leipzig on Wednesday.
Similarly, United boss Louis van Gaal wants to get the player on board so he can join them on their pre-season jaunt to the USA. The club have already made a £20 million bid to this end, but will likely have to up this to £25 million if they want to complete a deal for the France international.
If the Old Trafford outfit do manage to bring in the Frenchman, he will be their second summer signing after acquiring Memphis Depay from PSV Eindhoven. The 21-year-old fired the Dutch side to the Eredivisie title with 25 goals in all competitions, and the Red Devils will be hoping he can have the similar impact in the Premier League next season.
Schneiderlin would fit in in defensive midfield at Old Trafford, a position that van Gaal has identified as a priority according to the Metro.
With Michael Carrick now 33-years-old and Daley Blind often being used in defence, the role could be important as they look to compete on four fronts in the next campaign. The added matches from qualifying for the Champions League could be a real strain on what is a developing squad.