They are set to battle Serie A rivals AC Milan and Morata's former club Juventus for the forward's signature, though no deal will be struck until the Blues tie up their current managerial situation.
The 2016-17 champions will not sell Morata for anything less than the up-front fee of £58 million (€66m/$77.5m) that they paid Real Madrid for him in the summer of 2017, and while the player himself could yet push for an exit, the Stamford Bridge hierarchy will wait for Antonio Conte's successor to make the final decision.
Morata's agent, Juanma Lopez, met with all three Serie A clubs this week during a trip to Milan following the news that his client would not be part of the Spain squad at this summer's World Cup.
Though it is understood that Morata himself did not attend any of the meetings himself, he was photographed in conversation with Juventus sporting director Fabio Paratici outside Hotel Palazzo Parigi in a fashionable part of Milan on Wednesday in what is being described as a chance meeting.
Morata, 25, previously spent two seasons on loan with the Bianconeri - scoring 27 goals in 93 appearances - and adapted well to life in Italy as he learned the language and he met his wife, Alice Campello.
While Chelsea are totally closed to the idea of selling their club-record signing just 12 months on from his purchase, owner Roman Abramovich is keen to ensure the club remains as profitable as possible.
The feeling among the Blues hierarchy at present is that Morata just needs time to settle in London, with a back injury midway through the season impacting his form as he ended the campaign being used mostly as substitute, returning just 15 goals from his 48 appearances
He came off the bench for Chelsea's FA Cup final win over Manchester United on Saturday - a game which remains highly likely to be Conte's last one in charge of the club.
It is still expected that the former Italy boss will depart in the coming days, with Maurizio Sarri the frontrunner to take over following his departure from Napoli on Wednesday.
Additional reporting by Romeo Agresti.