The Spain international limped off during Chelsea’s 1-0 defeat against Manchester City on Saturday evening.
Morata, 24, pulled up midway through the first half.
And according to the Daily Express, the striker faces a lengthy spell on the sidelines.
They reckon Morata could be absent for up to two months with his hamstring injury.
The striker has been sensational following his summer move from Real Madrid.
Morata has netted seven goals in eight games under Antonio Conte in all competitions for the Blues.
The ex-Real hitman withdrew from the Spain squad this week following the injury against City.
Morata underwent tests on his hamstring in Madrid today, with doctors confirming he has a grade II hamstring problem.
Blues boss Conte was adamant that he won’t play for his country in their two World Cup qualifiers.
“It’s a muscular problem,” the Italian said.
“I don’t think it’s a serious problem because he stopped. He said he would prefer to stop and not risk a bad injury.
“The doctor now has to check the situation but I don’t think he’s available for the national team.”
Chelsea prepared to offer €5m a year deal to Serie A left back
Chelsea are prepared to offer Napoli left back Faouzi Ghoulam €5m a season to make the switch to Stamford Bridge, according to Le Buteur.
The Algerian publication say that both the Blues and Atletico Madrid are ready to double the contract offer made by Napoli. Naples newspaper Il Mattino reported last week that the Serie A league leaders had offered the Algerian international €2.5m a season to stay at the San Paolo. The defender’s current contract expires at the end of the season.
Le Buteur however say that Ghoulam will reject a new deal, forcing Napoli to sell him in the January transfer window. This could however open the door for Manchester City.
City played Fabian Delph at left back against the Blues on Saturday, and the long term injury sustained by first choice Benjamin Mendy could force them into the market in January, putting them in direct competition with Chelsea for Ghoulam.