This is according to the Mirror, who claim Antonio Conte's search for Diego Costa's replacement has lead him to the Real Madrid striker.
United had previously reached an agreement in principle to sign Morata, subject to settling on a transfer fee, but Ronaldo's supposed availability has thrown a spanner in the works.
There are rumours that both players could arrive at Old Trafford this summer in a deal that involves David de Gea leaving, but that remains to be seen.
Nevertheless, Jose Mourinho will be all too aware that he must make a decision soon given United's history with Chelsea when it comes to transfer sagas.
There have been five examples in recent memory of the Red Devils coming so close to signing a player but ultimately losing out to the Blues. Check it out.
Chelsea signed Eden Hazard for £32 million in 2012 and, five years on, he's proved one of their best ever signings.
However, prior to arriving at Stamford Bridge, the Belgian held talks with Sir Alex Ferguson and came close to joining before deciding Chelsea had the "best project".
Like Hazard, Arjen Robben also had discussions with Ferguson about playing for United and was even given a tour of Old Trafford with his father.
But then he spoke to Claudio Ranieri, who was later sacked but managed to convince the Dutchman of choosing west London instead.
United fans will forever blame Ed Woodward for failing to sign Pedro from Barcelona in 2015, having flown out to Spain to finalise the deal.
Pedro's agent claimed at the time that United and Woodward "fell asleep" during negotiations, whereas Chelsea were proactive and got the job done quickly.
Another player who slipped through Ferguson's fingers. United were told by Marseille in 2004 that Didier Drogba would cost them £25 million, which they deemed to steep.
Chelsea, on the other hand, were more than happy to splash the cash, and so they signed the Ivorian striker before Fergie could even made a decision.
JOHN OBI MIKEL
Missing out on John Obi Mikel wasn't exactly a disaster for United, but the Nigerian midfielder had signed a contract in 2005 and even wore their shirt in a press conference.
He eventually joined Chelsea, though, with the Blues paying £4 million to Lyn and a further £12 million in compensation to their rivals.
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