The North London outfit, who have not picked up a trophy since their EFL Cup triumph in 2007-08, have never before won the elite competition.
Spurs managed to take four points from a possible six against Los Blancos and they have already secured a place in the last 16 with two games to spare.
When asked by Omnisport whether Tottenham have a chance of winning the crown, Sherwood said: "Why not? Why not? They beat the champions there, didn't they? I'm not buying it was an off day [for Madrid].
"I think Real Madrid are a team on the down and they need freshening up. But they're still absolutely fantastic and Tottenham outplayed them. And I thought at the Bernabeu they were outstanding as well.
"Why not? They'll take a lot of belief and a lot of spirit with the performances they've done in the Champions League."
Spurs will secure their place at the top of Group H if they defeat Dortmund this evening.