Per the source, the Black Eagles have a five-man striker shortlist with Balotelli being one of the players the Super Lig champions are keen on signing.
Besiktas suffered a blow to their plans for next season after star striker Mario Balotelli revealed he will not be returning to the club.
Gomez finished last season as top scorer in the league and played a key role in the Eagles winning the league title.
Reds boss Jurgen Klopp told striker Balotelli that he has no part of his plan for the club according to the Mirror.
On Tuesday Klopp stated that the Italian international has dropped too far down the pecking order to get a starting role at the Premier League outfit next season and that the club will have to discuss his exit.
“With a lot of players it is not the moment to talk of transfers as it could kill all talks by saying someone was 70 per cent to sign him or whatever,” Klopp explained, per the Mirror.
“But I can talk of Mario because that one is obvious and I have spoken to him about this.
“He’s not at the stage of his career where he should be battling with four or five other players for one or two positions.
“We want him to become the player he was before his injury and the talent is still there, there’s no doubt about it. When we have done the crossing, heading and stuff in training, he has been world class.
“But this is not a situation where he should be battling with other players like this for one position, so it’s clear we need a solution.”
Besiktas finished last season as champions and can guarantee Balotelli Champions League football next season.