Roma are anxious to try and keep Strootman who was playing the best football of his career until his injury.
He only joined the Italian club from PSV Eindhoven last summer in a transfer worth around £16 million.
But it’s believed he would love to link up with his international manager at Old Trafford and is also close friends with United striker Robin van Persie, likely to become the club’s new skipper.
Van Gaal hopes that Roma will accept the offer for a player who will miss the first couple of months of the new season.
United have also been in talks with Paris Saint-Germain over striker Edinson Cavani but they are not as advanced as in the potential deals for Strootman and Hummels.