Interim boss Ralf Rangnick is also due to move upstairs when his short-term contract as manager comes to an end in the summer.
A number of former players have been critical of the situation at Old Trafford both on and off the pitch in recent years, with Evra among those to have questioned the change in culture at the club.
The 40-year-old previously hinted that he has been in talks with Man United over a role at the club in the past, and he has now claimed that he was offered the sporting director post.
"I passed my coaching diplomas and received lots of offers, including becoming a United sporting director," Evra told L'Equipe.
Evra made 379 appearances for Man United between 2006 and 2014, helping the club to win 14 trophies including five Premier League titles and the 2007-08 Champions League.