The France Under-21 international is eager to make the move and hopes to arrive in Leeds as soon as possible for a medical.
As previously stated, Hoffenheim were seeking around £35 million in total, including add-ons, which explains the lengthy negotiations.
Even at a lower price, it will still exceed the £27m club-record fee Leeds paid for Rodrigo from Valencia.
Rutter did not play in Hoffenheim’s recent mid-season friendlies, and their director of football Alexander Rosen dropped hints at his impending departure when asked about the situation.
“Ultimately we have to decide what is best for Hoffenheim under the given circumstances” he said.
“It is also important to include the thoughts of Georginio and those around him, because after all we are not talking about a piece of furniture here, but about the future of a young person”.
Leeds United currently sit 14th in the Premier League, two points above the relegation zone.