The Portuguese ace is currently plying his trade with Fenerbahce – alongside another ex-Anfield man in the shape of Dirk Kuyt – whom he joined from Chelsea in 2011.
Prior to turning out for the Blues he spent some time on the red half of Merseyside, and could be heading back to the North West of England from Turkey with the Toffees keen.
The 32-year-old has just over 12 months to run on his contract in Istanbul, but he could be offloaded this summer if a good offer is received.
Everton are said to be looking at him, with adding to his squad on Roberto Martinez’s agenda after a difficult campaign.
Meireles is an experienced midfielder who has represented Portugal on almost 80 occasions through his career, and has won titles in his homeland and Turkey.