Spurs beat big-spenders City to fourth place - and Champions League qualification - last season and Redknapp is determined to build on that achievement.
Manchester United, Chelsea and Arsenal are the only teams to have won the title since Blackburn lifted the trophy in 1995.
Redknapp knows that he needs to strengthen his squad further if Spurs are to break that dominance and he fears City will block his attempts to sign Craig Bellamy.
He said: "It is about time somebody else won the championship. It is not impossible and that is what I will tell the players. Yes (it is a realistic aim).
"There is no point me looking anywhere else. The sky is the limit.
"We finished fourth last year and Tottenham will never get a better chance. If we stand still the others will pass us.
"We did great last year finishing fourth. This year will be even tougher."
Source: PA
Source: PA