Vieira, 33, is poised to leave Inter Milan this summer and Spurs have shown interest in signing him of late.
Reaffirming the speculation, Tottenham coach Redknapp is willing to land the French veteran, who has also expressed his readiness to make a London return.
"If he comes and plays well the fans will love him, why shouldn’t they," Redknapp told reporters.
"They’ll probably think they’ve got one over on Arsenal because we’ve taken one of their great players. It will even it out with Sol Campbell perhaps."
Legend
Redknapp stated the technical reasons that would prompt him to buy the injury-ridden Vieira, who missed a lot of action at San Siro in previous years.
“I think Patrick would improve us. He would give us a real presence in the team. He’s been there, he’s done it all, he’s a fantastic professional. He’s a leader,” added Redknapp.
“You need people who have been there and done it and won it and that’s what he would give you.
"He’s got a good contract there (Milan) but he’s definitely interested and I’m interested in him coming. The players will respond to him. He’s a proper professional.
"He was a legend at Arsenal and he wants to come to Tottenham to play, not for the money. The money is probably a third of the money he was earning at Milan.
"He wants to come because he wants to play football. He would bring an awful lot to our football club."
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