The 20-year-old, who was playing non-league football with Maidstone United less than two years ago, has also interested Arsenal but a deal has been agreed with United for the youngster to join them at the end of the season.
There are still stages of the transfer to be completed but Fulham boss Roy Hodgson insisted: "There is no doubt in my mind he's going to United. Terms have been agreed, he's going for a medical and will sign for them and will join them from next season."
Smalling performed well against Spurs but could not prevent Peter Crouch opening the scoring before the break and David Bentley wrapping up victory with a free-kick that deflected in off Bjorn Helge Riise.
Bentley has been desperate to leave Spurs and his performance could attract clubs needing a winger, although Spurs boss Harry Redknapp is prepared to give the player a chance providing he shows a good attitude in training.
"It's up to him," Redknapp said. "If he shows a good attitude and comes to work every day and plays well and works hard then I have no problems with him. That's all you ask."
Victory kept Spurs in the top four of the Barclays Premier League and the only negative aspect of the evening was Heurelho Gomes picking up a shoulder injury that will require assessment before the clash against Birmingham at the weekend. It was also the first time Gareth Bale has been in the starting XI for a Premier League victory.
"It's a strange statistic," said Bale on Sky Sports. "I'm happy to get it off my back and go on from here. It was one of those freak things. It didn't really bother me but I'm happy to get the win."
Tottenham have shown an interest in bringing in Eidur Gudjohnsen on loan for the rest of the season, but Redknapp believes West Ham have beaten them to the former Barcelona and Chelsea forward's signature.
"I spoke to his agent, he said he was going to West Ham, so I left it with the agent," Redknapp said. "I would take him on a loan. He would be good loan signing playing in different systems. "He's a good footballer and an interesting player on a loan but I think he's gone to West Ham."