The Fleetwood Town technical director is reportedly wanted at Everton.
Steinsson is said to have been offered a recruitment role at Goodison Park, after three years at Highbury.
It is claimed the former Iceland defender, who was briefly employed by the Netherlands outfit, AZ Alkmaar, before his 2015 appointment at Fleetwood, will work alongside the Everton director of football, Marcel Brands.
Brands himself arrived in England from Dutch football, leaving PSV Eindhoven for Everton in the summer.
Steinsson, who also spent four years playing for Bolton Wanderers, is claimed to have a knowledge of players which extends throughout Europe and the English Football League, from which Brands is looking to benefit.
Brands has already improved Everton's squad with the signings of Richarlison, Kurt Zouma, Lucas Digne, Andre Gomes, Yerry Mina and Bernard from clubs at home and abroad.
Are Everton finally heading back to the top with Brands at the helm?