Blues boss Antonio Conte has long been an admirer of Morata but failed to get the desired performance levels out of his struggling striker, who managed just 15 goals in 48 games in his first season in England.
The 25-year-old will be disappointed with his campaign, having been left out of Spain's World Cup squad and also having lost out to Olivier Giroud for a starting place in the FA Cup final win over Manchester United.
A host of clubs are interested in signing Morata, but it remains to be seen whether Chelsea would allow him to leave, particularly as there will be an unwillingness to give the west London club a chance to recoup their record €64 million (£58m/$77m) investment on him.
The clubs who want Alvaro Morata
In Italy, the former Juventus man is already well known and a return to Serie A is a possibility. Juve have publicly declared an interest in the striker, although no contact has yet been made with Chelsea.
The Italian champions are aiming to secure the €100m (£88m/$118m) signing of Cristiano Ronaldo, and that will likely mean they are unable to fund a move for Morata.
And a return to Italy would likely be of appeal to Morata, who has previously expressed his love for life in Italy, where he met his wife Alice Campello while playing in Turin.
Borussia Dortmund's search to replace Pierre-Emerick Aubameyang, who joined Arsenal in January, could also lead them in the player's direction. However, the Bundesliga club's sporting director Michael Zorc has previously revealed it would be difficult to lure the Spaniard to Germany.
"I'd still say that Morata is too expensive," he told Funke Media, and added with a smile: "Without knowing the exact sums involved."
Which club is best for Alvaro Morata?
Morata needs a club and a manager to show faith in him to unlock his undoubted ability. At 25 he is still young and isn't the finished article, with improvements around his mentality and finishing still needed to get him amongst the best in the world.
That remains the player's ambition and Chelsea might be the best option for him, although the uncertainty over who will manage the Blues next term continues to linger.
It is likely that Maurizio Sarri will be charged with getting the best out of Morata, having previously worked wonders with Gonzalo Higuain while at Napoli.
Juventus would undoubtedly continue to push for honours with Morata in the team, while Inter are positioning themselves to compete for the Serie A title. Milan, meanwhile, would likely build their team around the former Real Madrid striker, but the club's financial situation would be a cause for concern.
To leave after one season would be an admission of failure at Stamford Bridge and it may be best for Morata to prove that he can do it in England, despite the struggle to adapt in his first season.