The Magpies are keen to move the 32-year-old on this summer.
Gayle, who is settled in the north east and has proven pedigree at second-tier level, is on high wages, but with Newcastle open to letting the Londoner leave, a compromise deal regarding terms is expected to be thrashed out.
Tottenham Hotspur are reportedly in advanced talks to sign Djed Spence, who has been linked with Nottingham Forest, Arsenal and Brentford.
Proceeds from the big-money sale of Spence would fund Boro’s recruitment drive this summer.
The Teessiders, who have agreed a deal to bring in Blackburn captain Darragh Lenihan, are interested in a number of players including Viktor Gyokeres and Southampton’s Adam Armstrong, who has been linked with a loan move and Aston Villa youngster Cameron Archer.
Leeds United have submitted their retained list, with four players to leave the club when their contracts expire.
Laurens De Bock, Josh Galloway, Alfie Hughes and Bobby Kamwa will be released while academy graduate Nohan Kenneh has already agreed to join Hibernian when his contract expires this month.
De Bock has joined Zulte Waregem on a permanent deal after spending the last two seasons on loan there while Galloway spent the second half 2021-22 on loan at non-league side FC United of Manchester.
Hughes signed a professional deal with Leeds last summer, but joined Newcastle’s Under-23s side on trial in March.
Kamwa signed a two-year contract with Leeds in July 2020 and spent the second half of last season on loan at Dunfermline.
Professional terms have been offered to William Brook, Keenan Carole and Harvey Sutcliffe.