The French right-back was looking for a new club last month after finding his first-team opportunities at Arsenal limited this season.
Debuchy fell behind Hector Bellerin in the pecking order at Emirates Stadium and struggled to hold down a regular spot in the north London side’s first team.
The defender was linked with a host of clubs last month before he eventually ended up joining Bordeaux on loan until the end of the season.
However, the former Newcastle man has claimed that he was prevented from joining United because Arsenal did not want to “help out a rival”.
Debuchy is quoted as saying by Canal+: “I was disappointed, obviously. If I had the chance to go to Manchester United it would have been magnificent.
“Unfortunately it wasn’t the case. I discussed it with the coach too, who said that obviously he couldn’t help out a rival.
“Yes, I’m a little bit annoyed with him. It’s his choice.”
United were believed to be on the lookout for defensive reinforcements following injuries to the likes of Marcos Rojo and Luke Shaw this season.
Arsenal travel to Old Trafford to face United on 28 February.
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