PSV are not keen to let the 23-year old leave but could settle for a deal if the right price is struck between the two sides.
Along with United, the likes of Liverpool, AC Milan and Arsenal are also interested in the central midfielder but the side from Old Trafford are outright leaders.
Talksport believe that an offer of 18 millions pounds will be enough to tempt the Dutch side but whether or not the EPL champions are prepared to stump up that amount remains to be seen.
Strootman made 53 appearances in all competitions last season, scoring 9 goals and making 12 assists.
In other news, Man Utd are also close to the signature of Benfica defender Ezequiel Garay who is set to join with Nemanja Vidic the one to possibly make way.