But Spurs lost out due to Manchester City’s financial muscle, according to Redknapp.
Barry joined City in a £12million move from Aston Villa on Tuesday.
He told The Sun: “This week, I tried to sign Gareth Barry. I felt he would be a good addition for Spurs and I knew we had to make a decent offer for a top England player.
“Liverpool were also prepared to make a big offer. But we have both been blown out of the water by Manchester City.
“They offered a far bigger transfer fee and are giving the lad much bigger wages. We could not get near.
“It’s certainly not Gareth’s fault that he is being given such a massive contract.
“But I believe the game could do one thing. I don’t see wages or transfer fees going down but English football could start putting something back into the community.
“I’d like to see every manager and every player in the Premier League make a donation to charity from their monthly pay packets.”