Keane rejoined Spurs in a £12million deal before the winter transfer window closed following an indifferent six-month spell at Anfield.
The former Leeds marksman qualifies for a winners' medal having played in 16 league matches for Liverpool.
The Reds remain in with a good chance of ending their title drought, but the 28-year-old has no thoughts of what silverware he could receive from the club - only how Spurs get on between now and the summer.
Give it away"My brother is a Liverpool fan so I'd probably give it to him," he said when asked what he would do with his winners' medal if the Reds claim the Premier League crown.
"The way I look at it is that a medal means something when you are a part of the squad and involved in winning a trophy.
"When you are in and out of the squad and not involved in games, there are times when you don't feel part of it.
"Next month's Carling Cup final means more to me because I'm a Tottenham player now, even though I can't play.
"Liverpool is gone. It's the past. What happens there now is not my problem."
Catch Spurs in action against North London rivals Arsenal on Sunday live on Sky Sports 1 and HD 1.