Celtic want to sign Olympiakos right-back.
Elabdellaoui made his name in Manchester City's academy before leaving in search of first team football.
The Scottish Sun's report claims Celtic are planning a move for the defender, who is rated at £4 million.
Elabdellaoui has won three league titles with Olympiakos in the Greek Super League after joining in 2014 and is bidding to win a fourth this season.
He had a loan spell at Hull City two years ago, and while at City he spent time at clubs in Norway, Holland and Germany.
The 27-year-old is a Norway international, where he is a teammate of Celtic ace Kristoffer Ajer.
Celtic are in need of signing a right-back, with Mikael Lustig not the player he once was.
Having signed two strikers and a winger, fans will welcome the club addressing the position, although the jury is out on whether Elabdellaoui is the best option.