United are expected to be at the front of the queue for Ronaldo, who they originally signed from Sporting Lisbon in 2003.
That figure could be in the region of 150m euros if Ronaldo's advisers are to be believed, although Real Madrid are said to be demanding at least 350m euros.
Real Madrid have released a statement saying they had "full confidence" in their player, and that they were convinced he would prove his innocence.
The rumours of a possible transfer back to England by the two-time Ballon d'Or victor started after a report surfaced that Spanish authorities have accused the 32-year-old of avoiding £14.7m in taxes.
Reports in Portuguese newspaper A Bola report that the four time Balon d'Or victor has decided he wants to leave Spain this summer after accusations were pointed in his direction about tax evasion.
A Bola - the paper that first reported Ronaldo's discontent - says the decision he has made to leave Madrid is "irreversible".
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Paris Saint-Germain have also said they would match any asking price Real set for Ronaldo, so United would face some stiff competition if they were to try to bring their hero back home.
Madrid have expressed "full confidence" in Ronaldo and believe he will be proven innocent of any wrongdoing, but nonetheless the Portugal worldwide is claimed to have made an "irreversible decision" to leave Santiago Bernabeu.
As one of the most marketable players in the world, Ronaldo's potential availability would generate much interest, but only the very richest clubs in the world would be able to afford him.
"I think it is very hard [to change his mind], Calderon said to BBC Sport".
After the report, worldwide media filled Portugal's training session in Kazan, where Ronaldo trained normally with the rest of the squad.
"I am sure he will stay in Europe", he said.