Two games before the end of the season, Spurs are one point behind fourth-placed north London rivals Arsenal and the Professional Footballers' Association (PFA) Player of the Year is optimistic of overhauling them.
"Everyone at Tottenham still believes it; we know it is not in our hands but there are a lot of funny things which can happen in football and there are two games to go," Bale told The Times of India.
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"I can see other teams dropping points so it can still happen.
"Since I first came to the club six years ago, when they showed me the plans for the club and what they wanted to do, it's been going forward," he added of Spurs' capacity to push on, top four or not. "There's been a progression ever since I've been here.
"I hope that continues and I hope we get Champions League football because that's what we all want and that's our target for the season."
After being named Footballer of the Year by the Football Writers' Association as well as the PFA, Bale says that he is humbled to join some exalted company.
"It's an amazing honour, especially when you look at the list of names that have won the awards before," he enthused.
"I got the award on Thursday and I sat there looking at pictures of all the previous winners and they are legends of the game. It's a dream come true to be up there with them. It's such a massive award, a historic award."
Asked about his favourite goal of the season, the attacker replied: "There's been a few but probably my winning goal against West Ham [on February 25], that's the one I'd pick."