The midfielder suffered an ankle injury in training in September with hopes that he could return to action after the October international break.
However, the youngster now looks set to be out under late November at the earliest, with the Blues expecting him out until December.
The Mail report that Chelsea are being cautious about his return and do not want to rush him back.
Lavia was close to making his Chelsea debut after completing a £58million move from Southampton, however the injury suffered in training has seen those plans shelved.
The 19-year-old suffered ankle ligament damage, meaning that he needed to wear a protective boot.
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That was removed last week, with Lavia doing some rehab work in the pool as he stepped up his recovery.
Despite that positive step, it's expected to be some time before he's out on the training pitch with his Chelsea teammates.
After seeing off competition from Liverpool over the summer, the Blues will be hoping that their big-money signing can be available for selection before long.
"I don't believe [he will be back after the international break]," Mauricio Pochettino said on his return.
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"I cannot tell you, but he is still not running. After the international break, he is not going to be ready, Romeo."