The Toffees want to appoint a successor to Rafael Benitez after sacking the Spaniard on Sunday amid poor results and the club tumbling down the Premier League table.
They have settled on Martinez, a former Everton manager, as a leading contender and are now taking steps to try to bring him in.
The Merseyside giants have contacted the Belgian FA to open talks over appointing Martinez, who they sacked in 2016 amid fan protests.
Martinez is their number one choice to take over at Goodison Park.
However, amid a host of managers being linked with the job, Everton are prepared to consider alternatives if Belgium refuse to let him go.
Martinez has qualified Belgium for the 2022 World Cup in Qatar next winter.
Losing him would be a big blow for Belgium and it remains to be seen if Martinez is ready to pass up the opportunity to manage at the World Cup finals.
