Damari has banged in 14 goals for Hapoel Tel Aviv in the Israeli Premier League this term.
But Hapoel officials are keen to offload their most saleable asset after running into financial difficulties following their exit from the Europa League.
Celtic were linked with a move for the forward when he was a player at Maccabi Petah Tikva two years ago.
The Parkhead club agreed a fee for the player only for him to move to Hapoel.
The 24-year-old has a €3million sell-on fee in his contract, but would be available for less than that to the Scottish champions.
Lennon has made securing the services of another frontman a priority during this transfer window.
He has been linked with Sunderland hitman Steven Fletcher and Wolves player Leigh Griffiths among others in recent weeks.
Damari is represented by the same agent who brokered the moves Beram Kayal and Nir Biton made to Celtic, and his team were understood to be in Glasgow last night.
Meanwhile, Charlie Mulgrew insists records mean little to the squad.
Celtic are more than halfway to achieving the first unbeaten season in the top flight since the 19th century and are only three clean sheets away from beating a club record of 10 consecutive shut-outs set in 1914 and equalled in 1922.
They are also looking for their 11th consecutive Premiership win when they face Hibs at Easter Road on Sunday, although they are some way off their own British record of 25, which they achieved under Martin O'Neill in the 2003-04 season.
But Mulgrew is more focused on winning the game in front of him than making history.
The Scotland international told Celtic TV: "We don't speak about clean sheet records or winning runs too much. We look to win the next game and if that means beating records then so be it."