Pre-season training starts on Wednesday and Martinez is yet to assemble his coaching staff as the club prepares for a new era under the Spaniard's management.
Assistant manager Steve Round, coach Jimmy Lumsden and goalkeeping coach Chris Woods have all been linked with a reunion with former Toffees boss David Moyes at Manchester United.
Martinez is set to bring in his own staff with Graeme Jones, his assistant at both Wigan and Swansea, likely to arrive in the near future.
"For Roberto to bring in his team is absolutely what he wants to do and we want to support him on it," said chief executive Robert Elstone.
"We are working hard to do that and I'm hoping in the near future that Roberto will have his team.
"He is also integrating into a very strong, solid team that already exists here.
"There is a real spirit at Finch Farm and lot of experience. I know he will want to retain that Everton spirit but yes, he does want his own support team around him.
"We are working to make that happen and I'm sure we will succeed on that in the very near future."
When asked about departures, Elstone said: "Whoever ultimately moves on to new pastures goes with our best wishes and our thanks for all their contribution they have made to Everton Football club."