The former England captain is set to leave Stamford Bridge in the summer.
The Chelsea captain looks set to end his life-long association with the club in the summer, after recently revealing that the club are not going to offer him a new deal.
He had said that he would not play for another English club in the future, with a move to the MLS, where former England teammates Frank Lampard and Steven Gerrard have moved in recent years, seeming likely.
But Redknapp has urged Arsenal to make a move for the former England captain, saying he would have tried his luck in the January transfer window also.
“If I ha been at Manchester City or Arsenal, I would have gone in on deadline day to see whether he wanted to move,” he told the London Evening Standard.
“Similarly, in the summer, City, Arsenal and Manchester United might look at Terry and see the benefit of signing him for a year.”
“Arsenal took Petr Cech, which many people thought inconceivable at this time last year, so why not John as well? He’d walk into Arsenal’s team even now – they need his character.”
The idea of Terry’s character being a good one for the Arsenal squad is certainly an interesting one from Redknapp.
More than anything he would bring a winning mentality to the side, with only Petr Cech in the current squad having actually won the Premier League title.
Adding that sort of influence into the side could be crucial for the Gunners, as the addition of Cech has been this season, but a move seems unlikely for both parties given the history involved.