Undav has been linked with an exit from the Seagulls, and the signing of Joao Pedro has raised questions about his future.
The 27-year-old made 22 appearances in the Premier League last season, but only six were starts.
Brighton manager Roberto De Zerbi also hinted about a potential exit for the German, insisting that other strikers are ahead of him in the squad.
“We will see what happens for Undav in the coming days in the transfer market, but Joao Pedro, Welbeck and Evan Ferguson are enough,” said De Zerbi (h/t BBC Sport).
Despite interest from several German clubs, Stuttgart appear to have won the race for Undav.
They are expected to sign Undav on loan with an obligation to buy, and the player has also given his nod to the move.
Undav will compete with Serhou Guirassy for the striker position in the starting XI, with the latter recently making his loan switch from Rennes to Stuttgart permanent.
Guirassy netted 11 goals in the Bundesliga last season and was crucial in Stuttgart avoiding relegation.
Stuttgart have also recruited young Serbian striker Jovan Milesovic this summer.
Brighton have been productive in the transfer window, signing Bart Verbruggen, Igor, Adrian Mazilu, Mahmoud Dahoud and James Milner.
Midfielder Moises Caicedo has been heavily linked with a move away from Brighton, with Chlesea undeterred in their pursuit despite having a £80 million bid rejected.
- Aston Villa mark European return with shocking 3-2 defeat to Legia Warszawa
- Nunez, Salah & Diaz secure Liverpool comeback win over LASK after early scare
- Tottenham to trigger Son contract extension to avoid another Kane situation
- Ineffective Man Utd star should be dropped for Burnley clash
- Daniel Levy open to selling Tottenham stake in Tottenham for ‘the right money’