The Leicester winger, 26, was given permission to leave Algeria’s World Cup squad to finalise a move before the window closed.
It appeared that his transfer had been lined up, but that was not the case and Leicester received no new offer for the player.
But the Starsport has been told that Mahrez’s representatives were trying to force through a move to Old Trafford.
They were aware United boss Jose Mourinho ideally wanted to add a winger to his squad.
The Italian club were demanding £48million, which United would not pay, and Mahrez’s advisors saw an opportunity to try to agree a deal.
Mahrez was the subject of a £31m bid by Roma but Leicester rejected that as they valued him at £50n.
He was also linked with Arsenal, Chelsea, Barcelona and Paris St-Germain – and was spotted in the French capital last Thursday.
But he is now staying with Leicester – at least until the January transfer window.