According to the Daily Record, the Norwegian international could be available for a cut-price fee because his contract expires in the summer of 2023.
Three years ago, Elyounoussi joined Southampton from Basel for £16million but failed to settle during a difficult first season.
He made just 19 appearances in all competitions as the club scrambled to survival after replacing Mark Hughes with Ralph Hasenhuttl.
The versatile attacker was then loaned out to Celtic, who he helped to win a domestic treble, albeit flitting in and out of the team.
Elyounoussi’s stay in the Scottish Premiership was then extended for a further year and he was one of the few bright spots as Neil Lennon’s side meekly surrendered the title to Rangers.
He registered 17 goals and eight assists overall, including a hat-trick in a 4-1 win over Motherwell and a brace away to Lille in the Europa League.
On his return to St Mary’s, Hasenhuttl resolved to give Elyounoussi another chance in the first team and he’s been heavily involved after impressing in pre-season.
Restricted to a spot on the bench for the opening two games, he starred in an 8-0 thrashing of Newport County to earn a place in the starting line-up.
A goal against Newcastle United followed in the first of a series of lively performances, leading to interest from Arsenal and Leicester.
Both see Elyounoussi as a budget alternative to their current attacking options, who would provide cover for a number of positions.
The 27-year-old is comfortable playing on either flank, or through the middle, and has a wealth of international experience.
He has 37 caps for his country and outshone Martin Odegaard with two goals in last week’s win over Montenegro, which keeps Norway on course for the World Cup.
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