However, Redknapp has also advised Arsene Wenger to make a move for the veteran centre-back in the summer, when the player should be a free agent.
Terry stated earlier this week that he will be leaving Stamford Bridge when his contract expires at the end of the season - although Chelsea have made it clear he could yet be offered a new deal - and Redknapp believes the 35-year-old would be a huge signing for Arsenal in particular.
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“If I had been at Manchester City or Arsenal, I would have gone in on deadline day to see whether he wanted to move,” Redknapp was quoted as saying by the London Evening Standard. “John could tip the balance in the Premier League title race for one of those sides.
“Similarly, in the summer, City, Arsenal or 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.”
Surely Chelsea will keep Terry for another year?
It’s hard to imagine Terry playing for another English club - he is Chelsea through and through - but the same could have been said about Cech and Frank Lampard.
If he has no desire to move abroad but still wants to play on, a move to London rivals Arsenal could suit the former England international.
Terry played every minute of Chelsea’s triumphant 2014-15 Premier League campaign and clearly still has plenty to offer.
It would subsequently come as a surprise if the Blues allow the fan favourite to walk away from the club as a free agent in the summer.
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