The talismanic forward, regarded as key to Tunisia's hopes of upsetting Belgium and England in Russia, was said to have been ruled out of the tournament after rupturing cruciate knee ligaments in a Qatari league game on Saturday.
However, Tunisian reports on Wednesday suggested the injury might not be as serious as initially reported and that the Al Duhail forward might yet be fit for the tournament.
"It could be a partial rupture, in which case we would proceed with a small intervention that would allow him to recover quickly," Tunisia team doctor Souheil Chemli told the daily La Presse on Wednesday.
Msakni was likely to fly to the U.S. for surgery in the next few days, his club said.
Tunisia have been drawn in Group G at the World Cup, where they open against England in Volgograd on June 18, before meeting Belgium in Moscow on June 23 and Panama in Saransk five days later.
(Reporting by Mark Gleeson in Cape Town; Editing by John O'Brien)
