Bamford joined Boro from Chelsea in January 2017, having previously enjoyed a successful loan spell at the Riverside, in which he scored 19 goals in 44 games during the 2014/15 season and was named Championship Player of the Season.
After something of a false start to his permanent career on Teesside, Bamford became a regular again last season and scored 10 Championship goals for Boro, including a first ever professional hat-trick in March of this year. Ironically, it came against Leeds.
They must have been sufficiently impressed with Bamford, as they are now interested in making him their first permanent signing of the summer, according to Sky Sports News.
The appointment of former Argentina and Chile manager Marcelo Bielsa had raised expectations at Elland Road, but two loan signings are all they have to show for their efforts so far this transfer window.
Bamford was tipped to be a future England star when he was on the books at Chelsea and playing for the Three Lions at youth level, but he never earned his way into the first team at Stamford Bridge and was repeatedly sent out on loan.
Leeds would be the ninth different club that the 24-year-old Bamford has represented in his career already.