Reports in Turkey claim United are preparing a £12m bid for Sneijder, who has also been linked with Premier League rivals Chelsea in recent days, says the Daily Star.
The Old Trafford side are set to test the resolve of the Turkish side with a bid worth double that of their summer offer.
Sneijder currently has a £13m release clause in his contract, but United look to be hoping to avoid activating it with a lower bid.
The 29-year-old currently earns £50,000-a-week in Istanbul, having agreed three-and-a-half-year deal in January this year.
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball