United are eager to wrap up the transfer before their first team players return for pre-season training at their Carrington training base in the second week of July, with manager Jose Mourinho keen to have his key transfer business done by then.
Recent reports suggested that Alvaro Morata had agreed a move to the Red Devils, with some publications even claiming the newly-married Spaniard ended his honeymoon early in order to finalise his move to the English club.
The 24-year-old has been subjected to transfer rumours linking him with a move to Old Trafford.More news: Coyotes get D Niklas Hjalmarsson in trade with Blackhawks
But Perez, when asked about Rodriguez, belligerently insisted that, should United sign Rodriguez, it would be for more than €80m.
James is largely expected to make a Madrid exit in the off-season, with Manchester United, Chelsea and AC Milan among those linked with a move.
"I have read that we have reached an agreement for I don't know for how many millions, but it is not true". We are still in June and until 31 August there is no need to hurry.More news: Led coalition says hit Islamic State targets in Syrian town
He feels there is still a lot of time for negotiations left in the summer, but warned Manchester United that Real Madrid are not the type of club who sell their best players easily.
"I do not want to undergo an interrogation".
Perez said the back-to-back Champions League winners had considered signing the France worldwide, but decided he was not needed in their first XI.More news: YouTube Celebrates 1.5 Billion Monthly Users, Announces Updates (GOOGL)
"He belongs to Madrid and Madrid players do not leave when they want to or their parents wants them to".