The deal could potentially rise to £10m with add-ons and ends speculation that Derby County’s Matej Vydra could be on his way to Elland Road after an impasse was reached over the player’s wages.
Bamford scored 13 times in 44 games for Boro last season and his capture would follow that of Scottish left-back Barry Douglas, 28, from Wolves, who has joined Leeds on a three-year contract.
Hull City will step up their search for defensive cover after former Tigers product and target left-back Conor Townsend joined West Bromwich Albion from Scunthorpe United.
City drew 1-1 at Barnsley with Jarrod Bowen equalising Kenny Dougall’s opener for the Reds.
Another target, Brighton winger and Czech Republic international Jiri Skalak, is in talks over a move to Millwall,
Sheffield United, who already have a £5m bid on the table for Ipswich Town’s Martyn Waghorn, are eyeing Liverpool striker Ben Woodburn.
Rotherham United are set to make a move for Glasgow Rangers midfielder Greg Docherty, 21.
He joined Rangers from Hamilton Academical on a four-and-a-half year contract in January and made 14 appearances last season.
Speculation continues that goalkeeper Kieren Westwood could be on his way out of Sheffield Wednesday.
He was again missing from the teamsheet as the Owls lost their final warm-up game 3-1 to La Liga side Villareal at Hillsborough on Saturday.
Former Cardiff City goalkeeper Ben Wilson, 25, who played for Telford in National League North last season, has joined Bradford City, who are also hoping to sign Blackpool right-back and free agent Kelvin Mellor.
Wilson recently had a trial with Shrewsbury but they have now signed Huddersfield Town’s Joel Coleman, 22, on a season-long loan.
That will leave Jonas Lossl and Ben Hamer, Town’s signing from Leicester City, fighting for the No 1 jersey.
Sunderland have yet to make an official bid for either of their two striker targets, Bradford City’s Charlie Wyke and Sheffield United’s Billy Sharp.