The Sun says Martinez will offer Baines a new deal - to try to keep him out of Manchester United's clutches.
And Everton chairman Bill Kenwright has warned off new Old Trafford boss David Moyes.
He said: "I've told David not to come back for him!"
Baines, 28, has two years left on his current contract and Martinez is determined not to lose any of his big-name stars.
The new Toffees boss said: "Leighton has been the best left-back in the league for a few seasons now and I'm really excited to work with him."