The Portuguese international could be back on Merseyside this summer.
The club have been linked with the player tentatively in the past but reports today claim they are actively pursuing the player, after Fenerbahce placed him on the transfer list.
The Turkish giants are looking to revamp their squad, which means getting rid of most, if not all, of their current foreign player quota. Dirk Kuyt has already departed on a free to Feyenoord, Emanuel Emenike is being offered to clubs and now Fener are hoping to lure Everton into a bid for Meireles, according to Turkish source Internet Haber Spor.
The report claims that Everton would have to pay €4 million to get hold of the player this summer.
Portuguese international Meireles joined Liverpool from Porto in 2010 and spent one memorable season at the club before heading to Chelsea in 2011.
The 32-year-old is certainly not as good as he was five years ago when he made his first move to England and for Roberto Martinez to bring in another player of such ilk to Everton would likely not go down well with fans.