But reports in Turkey claim Sneijder - who was also linked with a reunion with former-Inter Milan boss Jose Mourinho at Stamford Bridge - will be the subject of a £12m offer from United in the January transfer window.
The Netherlands international reportedly has a £13m release clause in his Galatasaray contract - but United hope to bring the Turkish giants to the negotiating table with a bid slightly below that figure.
Sniejder has been continually linked with a move to the Premier League - although Mourinho's connections with his former player mean he's often mentioned as a Chelsea target.
The Dutchman addressed these rumours last week, insisting he's happy in Turkey and intends to stay at Galatasaray.
But United, who have been lacking a creative presence in central midfield this season, believe they can persuade him to move to Old Trafford.
He reportedly earns £50,000-a-week at Galatasaray, which puts him well within United's wage structure.