The Foxes have been heavily linked with a swoop for the 28-year-old this month as boss Claudio Ranieri looks to strengthen his defensive options.
It was thought Leicester were hoping to land Acerbi for around £5million but Marseille's interest could put an end to the Premier League champions' interest.
The Ligue 1 giants have money to spend following their recent takeover by billionaire Frank McCourt and boss Rudi Garcia knows Acerbi well from his time managing in Italy with Roma.
Acerbi is under contract with Sassuolo until June 2018 but it is thought he would be keen on a move to either Leicester or Marseille should the Serie A side sanction a transfer.
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