By FOX SPORTS Staff
Spurs are currently fourth in the Premier League, four points ahead of fifth placed Arsenal and one point behind third placed Chelsea, albeit having played a game more than both teams.
Barring any unexpected results, Chelsea, Spurs and Arsenal are expected to be the only realistic challengers for the last two Champions League qualifying spot, with both Manchester United and Manchester City having established a comfortable lead ahead of the rest of the pack in first and second place respectively.
However, Graham, who previously enjoyed managerial stints at Arsenal and Spurs, has predicted the latter to miss out on qualification for next season's Champions League.
"Tottenham will be the ones to lose out," Graham told the Daily Mirror.
"They have a difficult run-in and they have played a game more than the others. [Arsenal] have recovered of late and it would appear they have the easiest programme to come.
"But I want to stress that it would be anything but a disaster for Tottenham or make it a poor season. In fact, I would say the opposite.
"Villas-Boas has been assembling a squad and he has done well to be in such a high position in the league and still be involved in the Europa League.
"He can build on that and I hope he can keep Gareth Bale - for the club's sake and the player's sake.
"It is unfair on Bale to compare him to the likes of Cristiano Ronaldo and Lionel Messi. He would really benefit from another season in England."
Graham also backed oil-rich clubs Chelsea and City to win silverware this season.
"Manchester City and Chelsea are parallel clubs," Graham added.
"There always seems to be drama on a weekly basis there.
"Chelsea, of course, are competing on three fronts with the FA Cup and the Europa League but they have the quality and numbers in their squad to compete.
"It is the same with City. They are also involved in the FA Cup but they have so many good players that they should be able to handle it and still finish behind Manchester United."
And with Arsenal failing to live up to pre-season expectations this season, Graham believes the club will spare no expense to bring quality players into the club during the summer to turn their fortunes around for their next campaign.
"Arsene Wenger would agree that much more was expected from Arsenal this season than just qualifying for the Champions League," Graham declared.
"I can see changes there in the summer with new players coming into the club."
Spurs will look to bounce back from their shock 1-0 defeat to Fulham when they take on Swansea in their next Premier League fixture.