The Inter Milan star has been linked with a move to both Old Trafford and United's rivals Manchester City.
But the midfielder appeared to have priced himself out a move by demanding ?200,000 a week.
In demand: Wesley Sneijder (centre) has long been linked with Manchester United
Now Sneijder is prepared to accept ?140,000, a wage that would make him the second highest paid player at United, behind Wayne Rooney.
The Old Trafford club are believed to have sounded Sneijder out about a possible deal but could not agree personal terms on the ?35million deal.
The Dutchman believed United would return with an improved offer but has now been forced to relent.
Sneijder claimed last week that he was keen on a move to United.
He said: 'Manchester United haven't made an official approach yet.
On his way: Samuel Eto'o is set to leave Inter for Russia
'But there have been unofficial talks, there have been contacts. But then there are always contacts.
'Thesituation is that I am now an Inter player, and chances are that I willstill be that come August 31. There is also a chance I could leave.
'Thatisn't really down to me but the club. I think Inter have been very clear: if a good offer comes in, they have to let me go.
'They don't want to lose me but there is a chance they will let me go.
Exit: Sneijder is believed to be keen to leave Inter this summer
'If something crosses my path, I have enough time to make my decision.'
But Inter vice president Adriano Galliani has said that he expects Sneijder to remain at the club, especially if Samuel Eto'o joins Russian side Anzhi Makhachkala.
Galliani said: 'There has never been any sort of negotiation for Sneijder. If Eto'o leaves then Wes will remain.
'But Sneijder was untouchable even before this Eto'o discussion began. But yes, even more so now. Sneijder will stay.'
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