The 23-year-old is out of contract but, amid interest from West Brom, Leeds' contract offer means a transfer fee can be awarded at tribunal.
Winger Pablo Hernandez, 32, has had his contract extended by a year after 38 appearances last term.
Goalkeeper Ross Turnbull is one of six players to be released by Leeds.
First-team players Jordan Botaka and Billy Whitehouse also leave, while under-23 players Jack Vann, Michael Taylor and Alex Purver depart.
New one-year deals have been offered to Eoghan Stokes and Tom Pearce and option have been taken up on the contracts of Conor Shaughnessy and Romario Vieira.
Meanwhile, for Taylor, who has been at Leeds since the age nine, any club he signs for would have to pay Leeds a fee related to his development as he is under the age of 24.
It has been reported that the Baggies have offered £3.5m in compensation for the player, who became the subject of internal disciplinary proceedings from Leeds after refusing to play in the club's final league match of the season.
Championship club Leeds United have offered Charlie Taylor a new two-year deal, despite the left-back's likely move away from Elland Road.