O Jogo says Fener are lining up a €10m bid for the veteran centre-forward in January.
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Fener see Muriqi as a potential replacement for Youssef El-Nesyri.
En-Nesyri is in advanced talks to sign with Saudi Pro League club Al-Nassr.
Mallorca, meanwhile, will be reluctant sellers given how important Muriqi is to coach Jagoba Arrasate's system this season.