Manchester United manager Louis van Gaal has refused to rule out the possibility of signing goalkeeper Victor Valdes.
Manchester City boss Manuel Pellegrini says he is confident that England goalkeeper Joe Hart will sign a new contract.
Ray Wilkins believes Wayne Rooney will have a better chance of winning trophies if he stays with Manchester United rather than joining Chelsea, and has urged the England striker to embrace the "healthy" competition for places at Old Trafford.
Former Red Devils manager Sir Alex Ferguson last season claimed the 27-year-old wanted to leave, and Rooney is understood to have been unimpressed by quotes from new United boss David Moyes this summer that suggested he would effectively have to be an understudy to main forward Robin van Persie.
Wilkins, who played for both clubs and has also coached at Chelsea, told talkSPORT: "It shouldn't end this way, it's getting horrible.
"Once you leave Manchester United there's only one way you're going.
"Man United are in the top three biggest clubs on the planet, therefore they will always buy and buy and buy because they always want to be successful.
"If you want to win things then there's no better club to be at than Manchester United.
"So what if you've got a bit of competition with Robin van Persie? It's healthy.
"He should stand up to the plate and show these people what he's made of. He's got so much wonderful football left in him."
United said yesterday their position remained that Rooney was not for sale.
Wilkins feels that should that stance change, the Red Devils would be "crazy" to let the player switch to another English club - although he admits he would personally love to see Rooney sign for Chelsea.
The 56-year-old said: "If I was David Moyes there's no way I would sell him to anyone in England. I'm sorry - he'd have to go abroad.
"I would love him to join Chelsea, though. I would love nothing more than to see Wayne Rooney wearing that blue shirt.
"I just think he's ready for his second coming. He's 27 years old and if for some strange outcome he stays in England, then Wayne is ready to start again.
"Man United would be crazy to do that though, they shouldn't sell him to one of their closest rivals."
Rooney was at the Barclays Premier League champions' Carrington training ground in Manchester on Tuesday morning.