Suarez quickly became a fans' favourite following a good start to his career at Anfield and he has continued to impress this term, scoring three times in Liverpool's opening five games.
Redknapp was desperate to sign a frontman in January after he realised Peter Crouch could not provide him with the goals his team needed to qualify for the Champions League again.
But Spurs balked at the £30million-plus fee they were quoted and Redknapp was worried that Suarez was too similar to van der Vaart, who the Tottenham manager likes to deploy in the hole just behind a targetman.
Having seen Suarez star up front on his own, Redknapp admits he probably should have pushed harder to bring him to White Hart Lane.
"We looked at Suarez," said Redknapp, whose side take on Liverpool on Sunday. "That was a player who we probably should have took, looking back on it now. The fee was £30-odd million and that's a lot of money.
"We thought he played a bit like Van der Vaart as well.
"We were looking for a targetman but I have seen him play up on his own and he can do that. He can play anywhere. He can do anything. He is a top-class, fantastic player."
Redknapp also revealed he was seriously interested in signing Carroll before he left Newcastle for Anfield in a £35million deadline-day move.
The England striker has struggled to make an impact at the Merseyside club due to lack of form and fitness and national boss Fabio Capello recently criticised the 22-year-old's lifestyle.
Redknapp is a big admirer of the player, though, and is wary of the damage he can cause to his patched-up defence on Sunday if selected.
"He is a real handful," Redknapp said. "He is a great header of the ball.
"When you go up against him you know you have had a game, that's for sure.
"We thought about signing him but we weren't in to spending £35million on one player."
Suarez and Carroll are just two of a number of players Kenny Dalglish has signed since he replaced Roy Hodgson as Reds boss halfway through last season.
The Scot has spent over £50million this summer on the likes of Stewart Downing, Charlie Adam, Jordan Henderson, Jose Enrique and Sebastian Coates.
Spurs just pipped Liverpool to fifth place last year, but Redknapp thinks Dalglish's spending spree means their rivals will be challenging for a top-four position come the end of the season.
"This is a big game for us," Redknapp said. "It will be them, us and Arsenal scrapping it out for the Champions League this year.
"They have spent a lot but they got £50million for Torres.
"They have wealthy owners and they want to be back where they were .
"Liverpool is one of the greatest football clubs in the world and they don't want to be out of the Champions League. They want to be back in there. They have invested trying to do that."
After two humbling defeats to both Manchester sides, Spurs picked up their first points of the season last weekend when they beat Wolves 2-0.
Ledley King, making his first start of the season after having knee surgery this summer, starred at Molineux and is likely to start alongside Younes Kaboul in defence on Sunday.
King's chronic knee problems have restricted his appearances in the last few years, but Redknapp is desperate to have his club captain available after Michael Dawson suffered an Achilles injury.
"We need Ledley. Dawson is out long term," Redknapp added.
"Ledley hasn't done anything all week. He will train Saturday, hopefully.
"He will come and have a little jog for about 10 minutes and he will hopefully give us the thumbs up and say he's fit."