The Manchester Evening News claim United are keen to tie up a deal for the Southampton man before the south coast club jet off to Austria for a pre-season tour.
Louis van Gaal wants everything rubber-stamped before his own side's trip to America later this month.
An offer of around £20million has reportedly been turned down as the Saints value the midfielder closer to £25m. And United could be set to test their mettle with an improved offer.
Van Gaal has been frustrated in his summer transfer endeavours so far.
GETTY
Morgan Schneiderlin (left) looks set to join Manchester United
Invalid email
We use your sign-up to provide content in ways you've consented to and to improve our understanding of you. This may include adverts from us and 3rd parties based on our understanding. You can unsubscribe at any time. Read our Privacy Policy
Holland international Memphis Depay was snapped up from PSV at the start of the transfer window but remains the only new addition as attempts to bring in reinforcements have hit complications.
Real Madrid star Sergio Ramos remains a top target and Bayern Munich pair Thomas Muller and Bastian Schweinsteiger are reported to be on the United boss's radar.
The Dutchman is keen to ensure all deals are tied up before they embark on their pre-season tour. A swift move could ensure they claim his signature ahead of Arsenal and Tottenham, who have also been linked with the Frenchman.