The Hoops were linked with a potential move for the winger in January, and fans will be familiar with the Norwegian from earlier this season.
Elyounoussi has scored seven goals and one assist in 13 European appearances this season, including a goal in the 2-1 and 3-1 defeats of Celtic in Europa League group stages.
The 21-year-old started his career with Sarpsborg 08 before moving to Molde in 2014, scoring 54 career goals and providing 18 assists, whilst claiming five caps for his country so far in his career.
Molde have also finished sixth in the Norwegian Tippeligaen, ruling the club out of European competition next season, while Celtic are still fighting for a European place come next season.
With his stock rising, the Norwegian, who scored a stunning volley against Celtic at Paradise earlier this season would cost around£2 million.