The Red Devils were believed to be monitoring Crystal Palace star Aaron Wan-Bissaka, but manager Ole Gunnar Solskjaer wants more experience in that position.
Diogo Dalot, 20, dubbed the best right-back in the world for his age upon his arrival last summer by ex-boss Jose Mourinho, has featured regularly under Solskjaer.
However, the Norwegian, who gave 33-year-old full-back Ashley Young a new deal in February, is still targeting Meunier, The Sun claims.
The Belgium international has started just five games since the turn of the year and is behind Dani Alves and centre-back Thilo Kehrer in the pecking order
Meunier, 27, is a huge Manchester United fan and has travelled to Old Trafford to watch them play this season.
Wan-Bissaka, who is also reportedly being chased by Manchester City and Borussia Dortmund, is rated at £50million.
He has started 30 of Crystal Palace’s 33 Premier League games this term.
And Meunier is seen as a cheaper alternative to the 21-year-old.
Solskjaer faces a defensive crisis ahead of their crucial game against West Ham on Saturday, which is live on talkSPORT.
Full-backs Young and Luke Shaw are suspended, while Antonio Valencia is not fully fit.
“We don’t have full-backs this week,” Solskjaer said.
“Not too many as we’ve lost Luke and Ashley through suspension. Antonio is still not fit.