And Southampton, who had looked to be out of the race, are in fact now closest to the USA international.
BILD reports that the Saints are offering €22m, more than previously thought.
Southampton’s bid is very close to Schalke’s €25m asking price and could be accepted.
A good relationship between Saints boss Ralph Hasenhüttl and Schalke sporting director Jochen Schneider could help.
The two worked together in the past at RB Leipzig and that should help negotiations go smoothly.
If Southampton do pay €22m for McKennie, he would become Schalke’s fifth most expensive sale ever, ahead of Breel Embolo and behind Manuel Neuer.
McKennie made 28 appearances in the 2019-20 Bundesliga season, scoring three goals.