Press Association Sport understands United's former Real boss Mourinho is keen to sign Morata as the Red Devils target three or four high-quality summer acquisitions.
The two also clashed during their time together at Real Madrid, making matters even more complicated.
"The clause for Cristiano is £1bn", he told Spanish Onda Cero.
While Ronaldo has yet to personally address the issue, his representatives have already denied the allegations and promised to soon show the public some documents that will prove the player's tax papers are clean and honest, according to Reuters.
And, although it is believed his stance has softened slightly after being backed by Madrid president Florentino Perez this week, his future remains shrouded in mystery.
Free-spending Paris St Germain have also been linked with a player that Perez insists there have been no bids for, nor he says has there been any offers for Alvaro Morata or James Rodriguez.
Geely acquires Proton stake and all of Lotus
Proton was formed in 1983 as part of an ambitious national industrialisation plan, but has suffered from a reputation for unimaginative models.
Real Madrid, for what it's worth, appears to be doing what it can to retain Ronaldo, with manager Zinedine Zidane reportedly reaching out to calm the star's worries and pitch him on staying put. "I have not spoken with him since [the Champions League final in] Cardiff".
Real Madrid star Cristiano Ronaldo has been in the news a lot in the last few days and it's not for all the good reasons.
"We don't have a guy who could compete with Messi or Cristiano for the Ballon D'Or, but I don't think we need a guy like that", Smolov said. "All this is very odd", Perez said. "I am sure that Cristiano complies with his tax duties, it must be a confusion that will be cleared", the Real Madrid president further explained.
Ronaldo joined Real Madrid from Manchester United in 2009 for a then-world record fee of 96 million euros and is their all-time top scorer with 404 goals in 394 games. The Spanish Supreme Court found Lionel Messi guilty of similar crimes previous year.
Speculations have been making the rounds about a possible return of Cristiano Ronaldo to Old Trafford.