The 22-year-old Argentine moved to Europe in 2018 when Stuttgart signed him from Argentinos Juniors and has attracted attention, with Leeds United keen on him during the last transfer window.
Gonzalez has five goals in the Bundesliga to his name this season and his performances have piqued the interest of several clubs for next summer.
A move in January is unlikely, but Stuttgart are likely to face pressure to sell him at the end of the season.
And it has been claimed Tottenham have already held talks over signing the forward in the next summer transfer window.
They have been joined by Juventus in the race and the Italian champions have also held discussions for Gonzalez.
But the discussions are still at a preliminary stage and no concrete plans have been made for Gonzalez by either club.
Tottenham are likely to consider adding depth to the forward area if they sell a couple of players in the summer.
Gonzalez is one of the names who is on their radar for the next few months as they plan for next season.