The Bosnia and Herzegovina defender had a scan after injuring his ankle in Thursday's 1-1 Europa League draw with FK Suduva.
The loss of Simunovic would leave Rodgers with only one experienced and recognised centre-back in Kristoffer Ajer for the game against the Accies.
"[Simunovic] has a scan this afternoon on his ankle," the Northern Irishman told reporters on Friday. "He was in pain when he landed so we will have to assess that late.
"I don't think Jack is available at the weekend. He played against Partick with a really, really sore ankle. In fairness to him he put himself out there to play and he was in too much pain. So he will probably come into training at the beginning of the week."
Forward Odsonne Edouard, meanwhile, could return in next Thursday's home leg against Suduva after missing the past three games.