The Daily Mirror is reporting that the Germany international has rejected a deal worth around £5m-a-year at the Bundesliga outfit.
Meyer is set to become a free agent at the end of the 2017-18 Bundesliga season to open up the possibility of a move in the summer transfer window.
The same article states that Arsenal, Liverpool FC and Tottenham Hotspur are all interested in signing the 22-year-old forward ahead of the summer.
According to the same story, La Liga leaders Barcelona are also monitoring Meyer’s situation given his impressive performances at Schalke 04.
Meyer has netted 22 goals in 189 games in all competitions over the past five seasons at Bundesliga outfit Schalke 04.
The attacker has scored one goal in four appearances for the German national team since making his debut in 2014.
Arsenal signed out-of-favour Bosnian defender Sead Kolasinac in a free transfer from Schalke 04 in the 2017 summer transfer window.
Liverpool FC brought in African defender Joel Matip in a free transfer from the Bundesliga outfit back in 2016 under current boss Jurgen Klopp.
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