The Hoops have had the 25-year-old watched, and have been impressed with the Israeli, who can play on either wing or just off the striker.
No bid has yet been made for the player, who is also attracting interest from the likes of Standard Liege, PAOK Salonika and Dynamo Kiev, but Ben Haim would likely cost in the region of £1.75 million.
Ben Haim learnt his trade at Maccabi Petah Tikva, before joining Hapoel Tel Aviv in 2012, before moving onto Maccabi Tel Aviv in 2013.
He has scored 57 goals in 242 matches in all competitions.
Maccabi Tel Aviv can count one-time Celtic midfielder Eyal Berkovic among their former players while ex-Rangers chief executive Martin Bain holds the same role at the club.
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