Villa have emerged as the surprise candidates to take fourth place ahead of Arsenal and set up a chance of mixing with Europe's elite in the 2009/10 campaign.
Tottenham, on the other hand, could conceivably be spending next season wallowing in the Championship, but Redknapp is confident that if his side can remain in the top flight, then huge improvements will be seen.
"For us be where Villa are? Hopefully next year," Redknapp said.
"I would like to be. If you are not looking that way then what are you aiming for?
"It's no good saying 'I hope we finish in the top half next year'. We have to hope for better.
"On our day, we are capable of giving anyone a game - we've got good players here and the club has invested heavily in the transfer window in the last few years.
"The size of this club, the potential, the fan base and the money invested, we should be pushing to get up there shouldn't we?"
Miss outWith Spurs set to face Villa on Sunday, Redknapp's charges could well strike a huge blow to those Champions League hopes by grabbing three points in the West Midlands.
Win, lose or draw though, the Tottenham boss does not expect their opponents to keep up their fine form to the end of the season.
"I think Villa will just miss out on the top four," he added.
"They have done very, very well and they're a good side, but Arsenal have got players coming back now, key players like (Theo) Walcott and (Cesc) Fabregas who will make the difference to them."