Meireles has six-months remaining on his contract and Fenerbahce are yet to renew his deal.
The Yellow Canaries are unlikely to extend his current deal which would allow him to leave as a free agent over the summer.
Aston Villa are however, unlikely to remain in top-flight football next season which could work against them in negotiations.
Villa face competitions from Portuguese giants Sporting Lisbon who are also reported to be in talks with the experienced midfielder.
Meireles has struggled to hold down a regular starting spot in the Fenerbahce side this season but has still made 18 appearances in all competitions.
The 32-year-old midfielder won PFA Fans’ Player of the Year in 2011 during his time playing at the Reds and went on to help the Blues win the Champions League and win the FA Cup.
Meireles signed for Fenerbahçe on a €10 million move from Chelsea in 2013 and has made a total of 84 appearances for the Yellow Canaries.