The Turner Stadium club have a lengthy shopping list ahead of the summer and understood to be keen on recruiting at least four or five new players.
Israeli national team midfielder Bitton is understood to be one of them, with one outlet in the country claiming HBS will make an approach for the player.
Bitton, 29, is under contract with the Hoops until the summer of 2023 but with a new manager taking charge this summer and the fall-out from a trophyless season, there could be a lot of comings and goings at Parkhead during the off-season.
Meanwhile, Hapoel Be’er Sheva remain interested in Hibs goalkeeper Ofir Marciano, who is set to leave Easter Road when his contract runs out at the end of the campaign.
An initial offer is believed to have been rejected by the 31-year-old shot-stopper but talks between the two parties will continue.
"Ofir will need a long contract that will secure his future,” the source is reported to have said. “There are more offers from Scotland and he hasn’t ruled out staying in the country. It all depends on the offer.”
Hapoel Be’er Sheva are also said to be keen on former Celtic and Brighton midfielder Beram Kayal but the 33-year-old is expected to remain at current club Bnei Sakhnin.