The Argentina international was wanted by Leeds United last summer and was keen to leave Stuttgart, but the Whites were not willing to match his asking price.
Having scored five goals from ten games in the Bundesliga this season, Gonzalez continues to attract interest from clubs across Europe.
Premier League giants Tottenham have been credited with an interest in the 22-year-old and have held preliminary talks, while Juventus are also said to be interested.
Interested clubs will need to wait until the summer to bid though as, according to regional German daily the Stuttgarter Nachrichten, Stuttgart are not under any sort of pressure to sell the forward this month.
The Bundesliga side believe they would be able to raise a larger fee for Gonzalez in the summer than they could this month.
The Argentine has a contract with Stuttgart until the summer of 2024 and his deal with the club does not include a release clause.
It remains to be seen if any of Gonzalez’s suitors test Stuttgart with a proposal before the transfer window closes at the start of February.