The Black Eagles sold last seasons top scorer to Shanghai Shenhua for €14 million and have yet to replace the Senegalese international. Ba found the back of the net on 28 occasions last term for the Istanbul based club.
The report goes onto state that while Arsenal have set a €14 million valuation on the England international, Besiktas want to negotiate a lower price.
Besiktas are also looking into the possibility of loaning the 24-year-old with an option to sign him at the end of the season.
Fikret Orman is expected to travel to London next week to hold talks with Arsenal and Welbeck.
Besiktas will only have two first-team strikers should they fail to sign another forward before the end of the transfer window.
Welbeck provided six assists and scored eight goals in 37 appearances for Arsenal last season.