The 33-year-old was strongly linked with a move to both Spurs and the Gunners last summer, only for him to eventually opt to remain at Inter Milan and fight for his place in Jose Mourinho's side.
However, with his first-team opportunities limited at the San Siro in 2009/10, Vieira has now decided to depart in search of regular action ahead of this year's World Cup finals in South Africa, becoming Roberto Mancini's first signing since arriving at Eastlands.
The Arsenal icon won three Premier League titles and four FA Cups during a successful nine-year spell under Arsene Wenger, making more than 250 league appearances.
But Redknapp has revealed that he came close to recruiting the Frenchman during the close-season, and was contacted again recently about the possibility of bringing him to White Hart Lane during the winter transfer window.
"I was very interested last summer. He was quite keen to come to Tottenham at the time," he said on Sky Sports News.
"I thought he showed a lot of character and a lot of bottle on his part to come and play at Tottenham, having been such a legend at Arsenal.
"It shows you what he was made of, to take that challenge on.
"It didn't happen. He got back in the squad at Inter Milan and the deal drifted.
"This time when he was available, I did get some phone calls about the possibility again but we felt that we had moved on a bit from there and that we were happy with what we had at the club.
"I'm sure he still has a lot to offer. He's a leader and a winner, and I'm sure he will do well at Manchester City."
NEWS: Vieira signs for Manchester City
NEWS: Domenech offers Vieira World Cup hope
