Leedsunited.com reports that 37-year-old Martyn, capped 23 times by England, has been given permission to speak to Everton boss David Moyes.
Peter Reid admitted that a deal was imminent after the 3-2 win over Middlesbrough at The Riverside Stadium.
Martyn has been kept out of the Leeds team under Reid by England keeper Paul Robinson.
And Reid, who has Danny Milosevic and Scott Carson as cover for Robinson, said: "He's in the last year of his deal and he has been a fantastic servant to this club.
"We've got young goalkeepers, that's one of the reasons for letting him go. But the other is as a thank you for being so patient.
"He is a top professional and deserves a first-team place somewhere."
Martyn, settled in the north, turned down a move to Chelsea at the start of the season.
The signing of Martyn will give Moyes the experienced goalkeeper he was looking for to provide cover and competition for regular number one Richard Wright.
Peter Reid admitted that a deal was imminent after the 3-2 win over Middlesbrough at The Riverside Stadium.
Martyn has been kept out of the Leeds team under Reid by England keeper Paul Robinson.
And Reid, who has Danny Milosevic and Scott Carson as cover for Robinson, said: "He's in the last year of his deal and he has been a fantastic servant to this club.
"We've got young goalkeepers, that's one of the reasons for letting him go. But the other is as a thank you for being so patient.
"He is a top professional and deserves a first-team place somewhere."
Martyn, settled in the north, turned down a move to Chelsea at the start of the season.
The signing of Martyn will give Moyes the experienced goalkeeper he was looking for to provide cover and competition for regular number one Richard Wright.