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The 20-year-old had impressed in his debut Premier League campaign, despite Southampton's relegation, and looked set for a big-money move.
Liverpool even agreed a deal with Southampton for the Belgium international but he preferred a move to Chelsea, who paid $73m (£58m/€68m) to take him to Stamford Bridge.
And Chelsea has since confirmed that the midfielder will not return before the end of the season.
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Boss Mauricio Pochettino revealed his thoughts on the injury in his press conference on Thursday, before Chelsea's clash with Burnley.
Then he trained and suffered a knock in his feet, then he got a quad injury against Crystal Palace."
Lavia had earlier shared a heartfelt note with Chelsea fans on social media as he bids to return to fitness in time for pre-season.
He said: "Hi Chelsea family.
See you soon."
Liverpool.com says: Lavia was always an expensive addition for the fee that Chelsea paid but it has been a nightmare signing given his injury woes.
Chelsea fans won't see him until next season and it does beg the question why he was signed if he had problems when he arrived at Southampton.
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