The Dutchman joined the Turkish giants from Anfield earlier this summer, and was quick to advise the 29-year-old to make the move as well, when the Portugal international made contact with him ahead of his transfer.
"Fenerbahce first reached an agreement with Chelsea and only then did I agree personal terms," Meireles stated to Lig TV.
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"We have a strong squad and are looking forward to playing in the Europa League. Everything is going fine. I'm physically in good shape and ready to play."
Meireles could make his Fenerbahce debut in Sunday's home game against Mersin Idmanyurdu.