However, Eintracht Frankfurt's demand of up to €60m may yet derail a deal that has otherwise advanced significantly.
Sky Sport Germany reported that Brown, 22, has had positive talks with Bayern Munich head coach Vincent Kompany and is keen to make the move to the German champions.
The personal agreement is considered a strong foundation, with the key remaining obstacle being the gap between what Bayern are prepared to pay and what Frankfurt's sporting director Markus Krösche is seeking.
Eintracht Frankfurt's valuation reflects the defender's market standing after an impressive Bundesliga season — four goals and four assists in 33 appearances — that attracted interest from Arsenal, Liverpool, Manchester City, Manchester United, Barcelona and Real Madrid, among others.
The Athletic had reported Arsenal as having Brown on their summer shortlist, making Bayern's move to secure personal terms a decisive intervention.
Whether the deal at €60m is achievable for Bayern remains uncertain. The source article notes the transfer could fall through purely because of the fee. Brown's contract at Frankfurt runs to the summer of 2030, giving the Frankfurt club full negotiating leverage.