The 24-year-old, who signed a new Tigers contract on Monday, has been out for 14 months with a groin injury.
Tuilagi gained two and a half stone on during a holiday in Samoa, weight he has now lost.
"The indications are good," said Leicester director of rugby Richard Cockerill. "January is not far away. I'd like to think he'll be near playing in the next few weeks."
Tuilagi's three-year contract makes him one of the Premiership's highest paid players.
Cockerill says he is worth the investment despite spending so long on the sidelines during a period when he was also convicted of assaulting two female police officers and a taxi driver.
"He is worth the gamble," he said. "He's been here a long time and has played a lot of rugby for us.
"Clearly he's had some injury issues but you have to support people through those situations. I've no doubt Manu will repay that faith by how he plays."
England centre Manu Tuilagi is in line to return for Leicester next month.