But it is Newcastle that have made the first firm move for his services as they look to give a considerable boost to Eddie Howe’s squad in an attempt to preserve their Premier League status.
The Magpies saw an initial loan bid rebuffed by the Red Devils earlier this week and have since returned with a similar offer.
It is believed the 13-time Premier League champions would prefer a permanent deal for the 29-year-old - but Lingard’s interest in a move to Tyneside is said to be limited to a half-season loan deal.
Speaking ahead of his side’s home game against West Ham, Rangnick revealed he is not surprised to see the midfielder attracting attention - but admitted the situation is not under his remit at the moment.
Ralf Rangnick confirms Newcastle’s interest
He said: “With regards to Jesse, it’s the same as quite a few other players.
“He’s a really good player, I can see that in every training session.
“For me, it’s normal that other clubs, for example Newcastle, show interest in him but I am not the one that is dealing with that.
“So there might be some interest from other clubs, but if you ask me now what will happen in the next ten days, until the closure of the window, I can’t answer that, I’m afraid.”
It is not yet known whether Lingard will be available to face West Ham at Old Trafford on Saturday afternoon.
The England midfielder scored the decisive goal as the Red Devils claimed a 2-1 when the two sides met at the London Stadium earlier in season.
However, he could miss out on a reunion with his former club as he continues his comeback from an ankle injury.