The Whites have been linked with a January swoop for the ex-Huddersfield Town man, who has been out of favour at the Riverside Stadium this season.
Clayton, who turned 29 on Sunday, started 13 Championship matches under former boss Garry Monk but has featured just once under Tony Pulis.
That was as a late substitute in a 1-0 home defeat to Fulham and reports have indicated Clayton will be allowed to leave in the January transfer window.
Pulis’ desire to cut an ‘over-sized’ and ‘imbalanced’ Boro squad has prompted many to conclude that the player’s days on Teesside are numbered.
Clayton scored six goals in 42 Championship appearances for Leeds in 2011/12.
Barcelona's highly-rated midfielder Robert Navarro is reportedly set to join Monaco on a five-year contract.
Japan enjoyed a dream start to their World Cup Group H campaign with a 2-1 win against 10-man Colombia in Saransk.
Huddersfield are set to step up their bid to sign Club Brugge forward Anthony Limbombe with a reported £13million bid mooted.
West Brom have been linked with a shock move for Jeremain Lens, who only joined Besikitas on a permanent basis earlier this month.