Besiktas have struggled up front since selling Cenk Tosun to Everton over the January transfer window.
Tosun scored more goals than first-choice striker Alvaro Negredo did all season and Vagner Love did not exactly set the league alight.
The Black Eagles have prioritized signing a new striker this summer.
Rangers forward Alfredo Morelos is being targeted by Besiktas to bolster their attacking force according to the Fanatik newspaper.
Per the source, Morelos has been added to the shortlist and the club are considering making a loan bid with a buyout option.
The Black Eagles are reportedly not prepared to match Rangers valuation and want to loan him on a temporary move before committing to a long-term deal.
The report claims that Rangers received an £11 million offer from China for Morelos but he turned down the offer as he does not want to play outside of Europe at this stage in his career.
The Colombia U20 international scored 18 times and provided eight assists in 43 appearances for Rangers this season.
Besiktas finish the league campaign in fourth place after being crowned champions the previous two seasons.