The Toffees may be without their young midfielder for up to five months after he picked up a medial ligament injury in training last week.
He consequently missed the 2-2 draw with Leicester City, and is facing a long period out of the first-team, which is a worry for Roberto Martinez.
With the England international having been set for a major first-team role on the back of a decent World Cup showing, a replacement is needed in the opinion of the Spaniard.
With not much time left in the transfer window Amalfitano has emerged as a target.
The Frenchman impressed on loan at West Brom last season and has since returned to Marseille, where he is understood to be no longer wanted.
At just £2m the 29-year-old is a tempting option for Martinez, who could swoop to beat QPR, Hull and West Ham to his signature.
Amalfitano produced a number of memorable moments last season for the Baggies, including a fantastic solo goal at Old Trafford in the Midlanders’ 2-1 win over Manchester United.