Sources have told ESPN FC there were concerns about the Argentinian forward's desire to join the club while United were not willing to meet his wage demands of £350k-a-week plus another £18 million in associated agents fees.
A move for striker Mario Mandzukic has not been completely ruled out but sources close to Juventus believe the relationship between the two clubs is now strained.
If Lukaku does leave, he is more likely to join Inter although there are serious doubts about whether they have the money to meet the £80m asking price.
Manager Ole Gunnar Solskjaer is open to the idea of replacing Lukaku before Thursday's transfer deadline but is also prepared to put his faith in 17-year-old Greenwood.
The forward, who made his senior debut last season, has impressed this summer after scoring goals against Leeds United and Inter Milan and there is a feeling within the club that he has earned the right to play a key role next season.
Real Madrid have expressed an interest in the midfielder but United chiefs do not believe they have the £180m it would take for the club to seriously consider an offer.
There is little interest in taking Colombia forward James Rodriguez or Gareth Bale as part of any deal as United believe they are players Real Madrid want to sell rather than names that would strengthen the squad.
Sources have told ESPN FC that Solskjaer feels he has had a positive summer after bringing in Daniel James, Aaron Wan-Bissaka and Harry Maguire while also leaving room in the squad for talented youngsters like Greenwood to get their chance.
Maguire's arrival means there are now seven centre-backs in Solskjaer's squad. Marcos Rojo could leave if he receives an offer that would guarantee more first-team football while United are also open to offers for full-back Matteo Darmian. The Italian defender is on the radar of Spanish champions Barcelona, sources told ESPN FC.
Chris Smalling's position is also vulnerable after he failed to play a minute of the final two friendlies of the summer. The 29-year-old signed a new contract in December and played 34 times last season but could now find himself down the pecking order behind first-choice defenders Maguire and Victor Lindelof.