"He's thinking: 'I had a great time at Arsenal and now I want to come and be a great player for Tottenham for a couple of years'," Redknapp said.
The 33-year-old France international had a distinguished career at Premier League Tottenham's north London rivals Arsenal and such a move would be highly controversial.
Vieira played 406 games for Arsenal in nine seasons, winning three league titles and three FA Cups, and it would be a major surprise for the fans of both clubs if he joined Spurs.
Asked if he was surprised Vieira wanted to come, Redknapp said: "Yes, it's a courageous move isn't it?"
"If he comes and plays well the fans will love him, why shouldn't they, and they'll probably think they've got one over on Arsenal because we've taken one of their great players.
