Spurs have moved to within three points of league leaders Manchester City after Wednesday night's 2-0 win over Everton.
"We're up there. We're in the Champions League mix and looking to do that. Who knows? Nothing's impossible, you have to keep believing and apart from that I enjoy the way we play. If you don't enjoy the way we play, then you shouldn't be watching football," Redknapp told Sky Sports News.
Spurs next host Wolverhampton Wanderers in the league on Saturday.