The Turkish Super League side are reported to have targeted Markovic after talks with Valencia over Feghouli broke down.
The Yellow Canaries are expected to part ways with striker Moussa Sow who is nearing a €17 million move to Al Ahli and will be looking to reinvest the money in strengthening the squad.
The Daily Star report that Fenerbahçe want Markovic on loan and that the Reds are open to the deal as the young forward has fallen down the pecking order at the club.
The Istanbul giants booked a place in the Europa League group stages following a 4-0 win on aggregated against Greek side Atromitos.
The Canaries also snapped up Brazil international Josef de Souza, Simon Kjaer from Lille, Turkish internationals, Ozan Tufan, Şener Özbayraklı, Volkan Şen and last seasons top scorer in the Turkish league Fernandao.