The 30-year-old defender who is available on a free transfer will however, hold talks with Rangers.
Taylor has however, yet to be linked with Fenerbahce in the Turkish press although the Yellow Canaries are currently in pursuit of defensive reinforcements.
Taylor has been at Newcastle for 13 years after joining his local side as a youngster in 2003. The experienced defender who can also play as full-back has struggled for playing time over recent years due to injuries.
Fenerbahce would be able to offer Taylor a lucrative deal and the lure of Champions League football.
The Yellow Canaries are currently managed by Portuguese head coach Vitor Pereira and finished last season as runners-up.
Taylor is almost certain to leave Newcastle following the Magpies relegation from the Premier League last season and the fact that he has not signed a contract extension.