Elabdellaoui, 27, plays for Olympiacos in Greece and is valued at around £4 million.
Right-back is a position that Celtic manager Brendan Rodgers wants to strengthen and he has been linked also with the Belgian international Timothy Castagne. However, the Atalanta defender has been valued at around £10m and is considered too expensive.
Rodgers is looking for long-term replacement for Mikael Lustig and Elabdellaoui could fit the bill.
Capped 34 times by Norway, he had a spell on loan at Hull City two years ago but returned to Olympiacos.
He began his career with the Norwegian club Skeid but joined Manchester City in 2010 when he was 16.
He failed to make the breakthrough at the Etihad and was loaned out to Strømsgodset, Feyenoord and Eintracht Braunschweig. He signed for the German side in 2013 before making the switch to Olympiacos a year later.
Elabdellaoui, who is of Moroccan descent, is under contract to the Greek club until 2021.