The 21-year-old recently admitted that there is only a "50-50 chance" of him staying in the Bundesliga next season after seeing his name linked with the Premier League pair.
Schalke sporting executive Christian Heidel was quick to play down a move away this summer, however, stressing that no formal approach had been made as of the end of March, but Meyer's refusal to pen a new deal may force his side's hand.
"I received an offer of a contract extension, but with my management I decided to turn it down," he is quoted as saying by German publication Bild.
When pushed on his next career move, he added: "That's the question. It's clear that I have to assert myself more next season."
Meyer, under contract at the Veltins-Arena until next year, played a part in two goals in 27 Bundesliga appearances during the 2016-17 campaign.