The 28-year-old enjoyed a prolific loan spell with Stuttgart last season, scoring 18 goals and registering 10 assists in 30 Bundesliga matches.
Undav established himself as an important first-team player for a Stuttgart side who exceeded expectations in 2023-24 and surprisingly claimed second place ahead of Bayern Munich in the Bundesliga, securing Champions League football for next season.
The Germany international has continuously expressed his desire to join Die Roten permanently this summer after recently admitting that he "never really got any appreciation from Brighton".
Undav claims "nobody cared" about him at Brighton
Undav joined Brighton for around £6m following an impressive two-and-half-year spell in Belgium with Union SG, scoring 45 goals in 70 appearances.
However, the striker has not quite made the grade at the Amex Stadium; he was initially integrated into Roberto De Zerbi's Seagulls squad for the 2022-23 campaign, but he only started nine of his 30 appearances in all competitions, scoring eight goals.
"The last year I was away, I never really got any appreciation from Brighton," Undav told German boxer Agit Kabayel, via Bild, last week.
"Nobody cared about me. That just showed me: Stuttgart really want me, they love me. Nothing came from Brighton for a year.
"I feel comfortable at Stuttgart. I would like to go to Stuttgart and hope that it works. Now it feels like they are negotiating every day. Let's see what happens."
Undav set to join Stuttgart for club-record fee
Negotiations between Brighton - now managed by Fabian Hurzeler - and Stuttgart over a deal for Undav have dragged for some time this summer, but the latter now appear to have made a breakthrough in their pursuit of their primary target.
According to German news outlet Kicker, Stuttgart have now reached an agreement with Brighton to sign Undav for €30m (£25.8m) plus add-ons.
Undav is expected to put pen to paper on a three-year contract and undergo a medical ahead of finalising his move back to Germany.
Stuttgart have the funds available to sign Undav for a club-record fee following the departure of last season's top scorer Serhou Guirassy, who has joined Borussia Dortmund after they activated his £15m release clause earlier this summer.
Meanwhile, it could soon be one German out and one German in for Brighton as they have reportedly made contact with free agent Mats Hummels over a sensational move to the Premier League club.