The Norwegian was out of contract at Southampton at the end of last season when the club were relegated from the Premier League.
He was not offered a new deal and the winger decided to move on from the club following the end of his contract.
His representatives have been holding talks with several clubs on behalf of their client and it has been claimed that he has found a new club.
According to Danish daily BT, Copenhagen are set to sign the winger on a free transfer in the ongoing transfer window.
He has been spotted in Denmark this morning ahead of him joining the Danish giants this summer.
Several other clubs such as Besiktas and Genoa were interested in him and he had offers from the Bundesliga and Saudi Arabia as well.
But following several rounds of negotiations, Copenhagen have won the race to sign him this summer.
Elyounoussi is set to complete the formalities of his transfer to the Danish giants soon.
