The Daily Star is reporting that Godin was offered a contract worth £6.3m (€7m) per season by the Red Devils – but the central defender has opted against a move to Old Trafford.
According to the same story, the 32-year-old defender was a target for Manchester United in the summer transfer window while Jose Mourinho was still in charge, but a move failed to materialise.
The same article says that following the latest offer, Godin has now ruled out a move to Old Trafford.
The story also suggests that Godin – whose current contract expires in the summer – could instead be heading to Serie A side Inter Milan.
Manchester United are likely to be linked with a number of players this month as they consider bolstering their squad at the midway stage of the season.
However, it remains to be seen whether they will actually do any business, with the club having only recently appointed Ole Gunnar Solskjaer as interim boss following the sacking of Jose Mourinho.
Manchester United will travel to Tottenham Hotspur for a crunch Premier League clash at Wembley on Sunday afternoon.
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