The 33-year-old has spent the majority of the summer on international duty at Euro 2024, where Germany were gunning for their fourth European crown.
Despite starting in a warm-up match against Ukraine on June 3, Gross failed to start any of Die Mannschaft's matches at the major tournament.
A deep-lying midfield duo of Toni Kroos and Robert Andrich kept the Brighton man on the bench for the most part, although the Seagulls skipper managed to make a substitute appearance against Scotland during the opening game.
Gross was a key figure at Brighton during the 2023-24 term, scoring four goals and providing 10 assists in 36 Premier League matches for Roberto De Zerbi's troops.
Dortmund closing in on Gross deal?
According to transfer specialist Fabrizio Romano, Brighton star Gross is set for a return to Germany seven years after departing FC Ingolstadt 04 for the English South Coast.
The report claims that a deal has been agreed between Dortmund and the Seagulls for the 33-year-old, who is showing no signs of slowing down at the top level of club football.
It is understood that last season's Champions League finalists will pay an initial fee of €7m (£5.9m) plus performance-related add-ons for Gross.
The paperwork for the deal is expected to be signed within the next 48 hours, meaning that Dortmund supporters could see their new signing unveiled before the conclusion of the working week.
Gross is expected to become Dortmund's third senior arrival of the summer following the signings of Stuttgart duo Waldemar Anton and Serhou Guirassy.
Brighton carry on without Gross
Due to his international exploits this summer, Gross was afforded an extended break by Brighton, meaning that he missed the opening of their pre-season programme.
Even if the 33-year-old was available for selection, it is doubtful that new manager Fabian Hurzeler would heavily play a midfielder who is clearly on the way out of the club.
Gross was left out of Brighton's squad for their pre-season tour of Japan, where the South Coast club picked up wins over Kashima Antlers and Tokyo Verdy.
The eight-time international has featured in 261 matches for the Seagulls over a seven-year spell, finding the net on 32 occasions and helping the club to qualify for European competition for the first-ever time.