England's veteran defender has been plagued by a back problem this season and the fitness concern has thrown his tournament selection into doubt. The 33-year-old may also miss out on the squad if he is unwilling to play alongside John Terry, who is facing a court case after the competition for allegedly racially abusing Rio's brother Anton.
Sir Alex revealed to reporters: "You play something like a game every four days at the Euros and Rio Ferdinand couldn’t do that."
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The United boss has also stated that his captain, Nemanja Vidic, will not be fit enough to participate in the club's pre-season tour of South Africa and the Far East. The Serbian has not featured since damaging his cruciate ligament in December against Basel.
The Scot added: "Vida won’t be going on the summer tour.
"He won’t be ready for that, but hopefully he will be ready for the start of the season. It's not been easy for him, he's not doing any running yet just work in the gym."