The 23-year-old has three more years remaining on his current contract with Stuttgart, but has been heavily linked with leaving the club this summer.
Premier League giants Tottenham have been credited with an interest in Gonzalez, while Italian outfit Fiorentina are also keen on the player.
However, Brighton appear to be edging closer to winning the race for the Argentina international, having agreed an initial £25m deal with Stuttgart.
The Bundesliga club have also accepted a similar offer from Fiorentina, but the forward is said to favour a move to the Premier League, giving Brighton the edge.
Should the deal go through, Gonzalez will become Brighton’s most expensive signing, with his transfer fee set to surpass the £17m the club paid for Alireza Jahanbakhsh in 2018.
While Tottenham have been heavily linked with the Argentine, it is unclear if they ever made a formal offer to Stuttgart.
Gonzalez, who has been on Brighton’s radar for a long time, scored six goals and provided two assists from 15 Bundesliga appearances for Stuttgart in the 2020/21 season.
The Argentine can operate on both flanks and as a striker, a trait that will appeal to Brighton boss Graham Potter.