Real exercised a buy-back clause to bring Morata back from Juventus a year ago.
Conte reportedly told Diego Costa, Chelsea's top scorer last season, that he was not in his plans for the upcoming campaign, leaving 23-year-old Michy Batshuayi as the only attacking option.
The Spain forward will discuss personal terms ahead of an expected move to Stamford Bridge.
The Spanish striker scored 20 times for Real Madrid last season, despite coming off the bench for the majority of the season.
REUTERS Francois Lenoir
It is believed Chelsea will pay around £70million to land Morata, That will set a new club record transfer for Chelsea, whose current highest outgoing fee is the £50m they paid for Fernando Torres in 2011.
And the £58m will make Morata the second most expensive Premier League signing so far in this transfer window.
Antonio Conte will have made Morata one of his highest priorities this summer, having worked with him at Juventus.
The Spain global rejoined former club Real after the European titans exercised a €30 million (£24 million) buy-back clause to bring the player to the capital once more, per Rory O'Callaghan of MailOnline.
The Everton man was Chelsea's top summer transfer target but boss Antonio Conte was left disappointed as the Belgium worldwide opted for Old Trafford and that has sparked the Premier League champions' interest in Morata.
It remains to be seen how much truth there is behind that report but the Mirror does say Danilo is looking to leave the Bernabeu due to a lack of first team football after starting just 17 league games a year ago.