Bale, 31, has returned to Spurs on a season-long loan from Real Madrid and is set to face West Ham on Sunday.
Redknapp managed Bale at White Hart Lane between 2008 and 2012 and says it will be “amazing” to see him back.
“For me he could be the difference this year for Tottenham,” Redknapp told BBC Radio Wales.
Current Spurs boss Jose Mourinho has said Bale will “probably” make his second debut for Tottenham on Sunday when they host West Ham.
Bale has been continuing his recovery from a knee injury since re-joining Spurs and missed Wales’ recent internationals.
Spurs are currently seventh in the Premier League and six points behind leaders Everton.
“Gareth coming back will make such a difference to Tottenham, he’s an amazing player.” Redknapp added.
“With [Harry] Kane, Son [Heung-min] and Bale that’s an amazing front three that could scare any team.
“I honestly think they’ve got a squad there capable of having a real chance to win the Premier League.
“You’ve got to fancy Liverpool and you’d have to fancy Manchester City, they would have to be favourites.
“But if anybody else is going to challenge them this year I think it’s Tottenham.”
Joe Rodon has joined Bale and fellow Wales international Ben Davies at Spurs following his deadline day move from Swansea City.
Redknapp says the switch to the Premier League is a “big opportunity” for the 22-year-old defender.
“Tottenham are short at the back and being a central defender it’s an area they could certainly improve over the next year or two,” he said.
“I speak to some people who work at Tottenham who followed him and monitored him and they speak very highly of him.
“I think there’s every chance he could go to Tottenham and have a great career.”