Spurs moved into fifth in the Premier League table with a hard-fought 2-1 win over Blackburn on Sunday and now trail Newcastle by three points with a game in hand.
Many people expect it to be a fight between Spurs, Liverpool and Arsenal for fourth with Manchester City, United and Chelsea tipped to fill the top three.
Redknapp has played down talk his side are favourites for fourth but is obviously targeting a return to the Champions League next season.
“I don’t know if we’re favourites, we’ve never finished above Arsenal before and that won’t be easy but we’ve got a good squad, good young players,” he said.
“We weren’t as strong as we’d have liked at the start of the season but City murdered us and they’re the team to beat. It will be tight.
“Chelsea will be there, United will be there, Tottenham could be up there, don’t write Arsenal off or Liverpool.”
Hibernian head coach Neil Lennon claimed Craig Levein's comments had come back to haunt him after his side's 2-0 victory over Hearts at Easter Road.
Rangers have been handed a boost ahead of the Old Firm derby at Ibrox on Sunday after Alfredo Morelos signed a new deal that keeps him at the club until 2021.