Spurs host Arsenal at White Hart Lane on Sunday looking for a win to stretch the gap to seven points over their arch-rivals.
Chelsea are also in the hunt to replace Tottenham in third place, and Sigurdsson expects the battle to continue until the end of the season.
"It is going to be a massive game for us," Sigurdsson said, looking ahead to the visit of the Gunners.
"However, anything is possible in football. The league was won in the last minute on the last day, so even if we beat them it is not finished.
"First, though, we have to beat them to start thinking about that. It will be a great atmosphere. Hopefully we can get a win and stay above Chelsea.
"We want to get in to the Champions League. That is our aim. If we achieve that, we want to finish as high as we can."