The Whites are continuing to push for fresh faces to come in at Elland Road after already bolstering the squad with the likes of Lukas Nmecha, Jaka Bijol and Sebastiaan Bornauw.
They have an agreement in place with Newcastle United for Sean Longstaff to join, but Daniel Farke wants another midfielder in through the door.
Hoffenheim star Stach is the man Leeds want and he has been open to a switch away from the German side this summer.
Leeds contacted Hoffenheim about Stach earlier this month and now they have upped the ante.
An agreement on personal terms is in place between Leeds and the player, according to German broadcaster Sky Deutschland.
However, Leeds face needing to agree to pay €20m plus add-ons as that is what Hoffenheim are demanding to play ball.
Leeds could try to negotiate that price tag down, but Stach is not short of interest and Hoffenheim have had enquiries from other clubs too.
Into the final two years of his contract, Hoffenheim could well feel that now is the right time to sell Stach and it remains to be seen how firm that asking price is.
The midfielder, who is due to turn 27 years old later this year, was signed by Hoffenheim from Mainz in 2023.
Stach has never played his football outside of Germany and Leeds will need to hope he can adapt to life in England quickly if he does make the move.
A product of Osnabruck’s youth set-up, Stach has been capped twice by Germany and may well hope playing for Leeds in the Premier League can push his case for more caps.