Chelsea have tabled a £62 million (70m euros, $80m) bid for the 24-year-old Morata but Real Madrid are holding out for around £80m, the reports say.
Chelsea have offered Morata wages of £150,000 a week on a five year contract, according to London’s Evening Standard.
Morata is keen to play for the manager and told The Guardian Conte had given him self belief.
Morata came close to playing for Conte at Juventus in 2014 when the latter played a pivotal role in persuading him to join Juventus…only for the coach to jump ship and take over the national side.
“I feel indebted to him because he’s the coach that most trusted in me, most wanted me, who made me feel I could perform at the highest level,” Morata told the newspaper in April.
“Yet I’ve never had the fortune to actually work with him. I’m sure sooner or later I will.”
Morata would replace fellow Spanish international Diego Costa, whom Conte told at the end of last season he no longer figured in his plans despite his 20 Premier League goals spurring on Chelsea to the title.
Costa endured a fractious relationship with Conte last season leading to rumours of him moving to China and then having to apologise to coaching staff after a training ground bust-up.
He is linked to a move back to Atletico Madrid even though they cannot register new players until January because of a blanket FIFA transfer ban.
Several newspapers say Chelsea have rejected an initial bid of £22m for the 28-year-old Brazil-born marksman — whose febrile temperament also played a role in Chelsea’s alarming slide in the 2015/16 campaign and to Jose Mourinho’s sacking — and would like to recoup at least the £32m they paid for him in 2014.
Regardless of whether the deal is done this week it is considered highly unlikely Costa will be taken on the club’s pre-season tour of Asia.
– ‘Further disappointment’ –
Morata had been thought to be Manchester United’s principal striker target until they swung towards 24-year-old Lukaku and spectacularly stymied Conte’s well-laid plans.
Conte, who has yet to sign along with his backroom staff the new contracts they were offered at the end of last season, is thought to favour another Spaniard , the veteran Fernando Llorente, as a fallback option should they fail to land Morata.
Llorente, who was signed by Conte when he was at Juventus in 2013, performed well for Swansea last season but at 32 would be a relatively cheap short term replacement for Costa.
Thusfar Chelsea’s recruitment for a season that will throw up the extra challenge on the squad of Champions League football has seen experienced Argentinian goalkeeper Willy Caballero join for free and German international defender Antonio Rudiger sign for £29m on Sunday.
There could also be further disappointment for Conte with regard to his pursuit of midfielder Tiemoue Bakayoko as several newspapers suggest United are ready to launch another commando raid to hijack the deal.
The Times and The Daily Mail say United are willing to offer £40m — matching Monaco’s valuation — rather than the £35m Chelsea bid for the 22-year-old.
Chelsea are loath to better the offer because of concern about Bakayoko having undergone keyhole surgery on a knee in the close season.
United had originally been keen to bring Nemanja Matic from Chelsea but The Times says the Lukaku affair has endangered that deal in souring the two clubs’ relations.