Morata has had a call in both the summer and winter transfer windows from the Chelsea manager, who has made it clear that he is a huge fan of the Spain international and that he is monitoring his situation.
The 23-year-old is happy in Madrid and determined to prove his worth as he battles for a starting role with the likes of Karim Benzema, Cristiano Ronaldo and Gareth Bale, but Conte is aiming to ensure that Chelsea are at the front of the queue should Morata grow frustrated over a lack of minutes on the pitch.
Conte tried to sign Morata when he was Juventus coach, but moved on to manage the Italian national team, with Massimiliano Allegri completing the deal soon after he left.
Madrid exercised a buy-back clause last summer to reclaim a player they developed through their youth system after two impressive seasons in Serie A.
Zinedine Zidane’s side have only used him sparingly so far this season, but Morata loves his home city and he is determined to prove himself, despite difficulties in his first season back.
Michy Batshuayi has failed to establish himself in his first season at Stamford Bridge since his £33 million move from Marseille in the summer, while Chelsea have also had issues with Diego Costa, despite his status as the Premier League’s top scorer.
Costa was dropped against Leicester by Conte after a bid from Tianjin Quanjian left him unsettled in January. He has since been reintroduced to the squad but he has yet to come to an agreement with the club over a new long-term deal.