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According the The Mirror the Bundesliga outfit have tabled a £150,000-a-week deal.
The contract also includes bonuses worth £1.75million a year and a £50m buy-out clause.
Goretzka, 22, is out of contract in the summer.
That means he’s free to negotiate a pre-contract agreement with foreign clubs from January 1.
Manchester United have emerged as serious suitors for his signature in recent days.
Barcelona, Manchester City, Liverpool and Arsenal have also be credited with an interest.
Arsenal player ratings v Manchester United
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“Schalke star Leon Goretzka is wanted by Manchester United ”
Nou Camp legend Xavi wants to see the in-demand strutting his stuff in Catalonia, though.
"I've seen him play and I think he's a good player," he said.
"Without doubt, he could play for any team the world.
"He would fit in well [at Barca]. Goretzka is a young player.
"Germany always have good footballers and he's one of them."
Schalke have previously insisted they will not sell the player in January and will risk losing him on a free in the summer.
Despite his relative youth, Goretzka has racked up over 100 appearances for Schalke.