Spurs are currently eight points behind Leicester City at the top of the Premier League table, but they have still have some hope that they could finish on top of the pile.
Although the Foxes managed to beat Swansea City comfortably in their last outing - Claudio Ranieri’s side still have matches against Manchester United, Everton and Chelsea to play.
Leicester need five points to ensure that they pull off the biggest shock in Premier League history, but Smith believes that Spurs will keep the pressure on.
The former Arsenal striker suggests that the Lilywhites will take 12 points from now until the end of the season, as they are in such good form currently.
“I think there’s every chance of that [they’ll win all four],” Smith said.
“The way they are at the moment - they blew away Stoke. And even against Chelsea, as much as the Chelsea players and fans don’t want them to win it, I think this season they’re a much better team.
“I can see them picking up 12 points there, without question.”
Tottenham’s will surely have to win every one of their matches to have any chance of clinching the Premier League title.
It means that they are under severe pressure ahead of their next match, which comes against West Bromwich Albion at White Hart Lane later this evening.
Spurs’ also have fixtures against Chelsea, Southampton and Newcastle United left to play this term.