The former Red Devil has been a star performer for the Toffees this season and is hopeful that he will be fit in time to face his former club.
Tom Cleverley is in a race against the clock to be fit in time for Manchester United’s visit to Goodison Park next month.
The Toffees midfielder had been in great form during the early part of the season, before an injury against Tottenham Hotspur left him sidelined.
Speaking ahead of Monday evening’s trip to the Hawthorns where they will face West Brom, in quotes covered by the club's official Twitter account, Martinez said that the duo are recovering well and that Cleverley is weeks ahead of schedule.
He said: “Tom avoided surgery and tomorrow he will be running on the grass and he wants to play against Manchester United.”
“That is a realistic target and is three weeks earlier than we thought. Leighton is the same.”
The news comes at a good time for Everton, with the Toffees boss also refusing to rule out involvement in Monday night’s game for John Stones.
The England defender was forced off with a knee problem during Tuesday’s Capital One Cup win over Reading, but has responded well to treatment.
Seamus Coleman will also be assessed ahead of Monday’s Premier League clash.