Tottenham were offered Van Bommel in the January transfer window when Bayern Munich decided to allow the 33-year-old to leave six months before his contract expired.
But the World Cup finalist, who also attracted interest from Liverpool, opted instead to join AC Milan on a five-month deal as Redknapp mulled over whether signing the 33-year-old would be worthwhile.
Tom Huddlestone's setback in his return from an ankle injury has left the Spurs boss with Jermaine Jenas and the erratic Wilson Palacios to choose from to protect his back four.
He believes that Van Bommel could have added an extra layer of steel to his squad towards the end of the season and admits he is considering an approach for the physical former Barcelona man when his contract at Milan ends this summer.
"I could have took Van Bommel, it was probably a mistake - perhaps I should have taken him," Redknapp said.
"It was a difficult one and I dragged my heels with it. I took my time over it, too long and we didn't do it in the end.
"He would have been a good player for us. Tom has had a setback and Van Bommel was on a free, he has signed a five-month contract at AC Milan.
"He gives you experience, he's been there, played Champions League final, World Cup final. He is a proper player for sure but that's how it goes.
"We could go back for him."
Redknapp was only able to land Steven Pienaar and Bongani Khumalo in what was originally expected to be a busy transfer window for the club.
Chairman Daniel Levy made club record bids for Sergio Aguero and Giuseppe Rossi but neither deal went through and Redknapp watched on as rivals Chelsea spent £50million on Fernando Torres and Manchester City splashed £27million on Edin Dzeko.
Redknapp admits he was surprised at the fees that changed hands last month, but insists that Tottenham can keep up with their big-spending competitors in the market.
"I had a look at Dzeko last year and they were talking £50million and that was too dear, then suddenly he looks cheap at £27million," Redknapp said.
"Ronaldo doesn't look dear at £70million when you look now. How much is Messi worth I wonder? He's got to be worth £1billion.
Redknapp believes that an unfortunate consequence of the money flooding the British transfer market is that the five clubs in contention for the Champions League will not do business with each other.
"Man City won't sell us a player," Redknapp said.
"We didn't bid for (Emmanuel) Adebayor because we knew it would be a waste of time."
Redknapp takes Tottenham to Bolton tomorrow knowing that a win will draw his side level with fourth-placed Chelsea, who play Liverpool on Sunday.
With almost two thirds of the season complete, Tottenham sit 13 points behind leaders Manchester United and eight behind their main challengers Arsenal.
A 4-0 hammering at Fulham in the FA Cup last week led some to question Tottenham's ability to make it into the top four again but after losing just once in their last 13 league fixtures, Redknapp insists his side can stay the course and are even good enough to finish third.
"We won't finish above Man Utd. If I had to pick one team who might have a chance of catching them I would go with Chelsea," Redknapp said.
"We have a chance to finish above the others.
"It's quite open. City are a good side but it's not impossible, and it's not impossible to finish above Arsenal.
"The belief is there. We have lost one league game since god knows when, at Everton. We can write the cup off, we had a horrific first 10 minutes at Fulham."
Redknapp has also revealed that Spurs have started talks with William Gallas' about renewing his contract beyond the end of the season.
He said: "I think it probably will get done.
"William wants to stay and he has been outstanding."