Jermain Defoe got the only goal of the game against the Baggies to maintain the team's impressive run of form which has seen them lose just once in their last 17 outings, while finding the net in 18 successive games.
The north London club’s form leaves them just three points away from United and six away from leaders City and with a game in hand still to play, Redknapp is feeling confident following a successful first half of the season.
"We're there or thereabouts," Redknapp told reporters. "We've just got to keep believing and keep going with it. You never know do you? Nothing is impossible.
"It's been a great first half of the season for us. The amount of points we've got has been amazing considering we lost the first two games. We've just got to keep going and see where we end up."
However, the win against Roy Hodgon’s side came at a cost as both Sandro and William Gallas failed to finish the game after picking up injuries.
"Sandro tore a calf, so that'll be a long one, and Gallas as well," Redknapp confirmed. "It didn't look very good. They'll have scans [on Wednesday]."
Hodgson himself is under the belief that Spurs can challenge for the title after pulling away from the teams behind.
"Spurs are serious title contenders and they are putting pressure on the two Manchester clubs to keep winning," he said. "They are getting some distance between themselves and the chasing pack of Arsenal, Chelsea and Liverpool."