The Blues had a bid for the United star, whom manager Jose Mourinho confirmed is his only remaining transfer target, rejected on Tuesday as he continues to angle for an exit from Old Trafford.
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Chidgey told Perform: "I'd have the Rooney of about five years ago like a shot, no doubt, because he was certainly one of the best players in England, if not Europe.
"But the Rooney of now? He seems, after he forced United's hand a few years ago, wanting more money ... I don't think he's been the same player for United since then.
"I worry that he's been playing at the top of his game for 10 years ... is he burning out? What's his motivation? Is it about playing for the money or playing for a team? He seems to fall out regularly with United - do we want that Rooney at Chelsea?"
Chidgey is aware that most players who leave Old Trafford do not tend to kick on in their career and feels that any acceptance from United of losing Rooney could be a bad sign.
"Manchester United are very, very good at selling their big players," he observed. "They very rarely let players go who they actually want to keep and they think who can do a job for them.
"If they're prepared to let him go, that suggests they've had enough of him and I'd be very concerned by that. Wayne Rooney might be angry and confused - I'm just confused."
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"I think, as a lot of supporters do, that we are in need of getting a top quality striker," he continued. "Maybe he's not performed at United because he's not happy there. Maybe he needs a new challenge. He's been there a long time, he's won an awful lot, maybe he needs to go somewhere else and get his passion back.
"We don't know whether [Fernando] Torres can ever be the player he was. [Demba] Ba came in to do a job in January and [Romelu] Lukaku, while he has the potential to be a Chelsea great, is still young so we need a striker and it may well be that Rooney is the only one available.
"I think we can win the title whether we get a striker or not. If you look at the amount of goals we can score elsewhere on the pitch, I still think we would be in with a good shout if we did nothing.
"Having said that, I think we would be in with a better shout if we did add to the striking department because it would make us stronger."