Rafael made 109 appearances for the Red Devils before joining Lyon in 2015 after Antonio Valencia’s move to right-back left him surplus to requirements at Old Trafford.
He has rotated with Kenny Tete this season, although their game time has been similar, with the young Dutch right-back playing only 200 minutes more than the Brazilian in Ligue 1.
With a third right-back in Leo Dubois set to join Lyon this summer, one of Rafael or Tete may see their time at Les Gones come to an end.
But Rafael, who is under contract until 2019, does not want to leave, telling Planete Lyon : "I would like to extend here because I like Lyon.
"I still have a year-and-a-half on my contract. And you can’t stay here with three right sides, you just have to leave one of the three sides.
"We will see the intentions of the club.”
The 27-year-old has been outperformed by his competitors this year, with both Tete and Dubois having four assists compared to Rafael’s one.
Dubois has been one of Nantes' standout performers this season and is joining Lyon on a four-year contract on a free transfer.