The Serbian midfielder has a contract until June 2014 at Weserstadion, which means he will be available at a cut-back fee in the summer.
Ignjovski is believed to be pondering his options after seeing little playing time in the first part of the season, although club chiefs are hoping he will accept a new contract offer after finally nailing down a regular starting berth.
Nevertheless, the 22-year-old has a €5 million release clause in his contract and Bild reports that Besiktas are ready to match the asking price in the summer transfer window.
The Turkish giants have been keeping close tabs on the talented midfielder for a while and they are eager to sign him before Werder offer him a new deal.
Ignjovski, who can also play at right-back, has scored 1 goal and produced 2 assists in 14 Bundesliga appearances this season.