Dacourt is currently playing for AS Roma, but is looking to move. He was a fans favorite during his one year at Goodison under Walter Smith, and has also played in the Premiership with Leeds United.
"We received an offer from England but the squad did not meet his satisfaction," The player's agent said said. "If a concrete proposal arrived this month then I believe the club would look at it seriously."
It is thought that Dacourt would cost in the region of £4m.