The two clubs have settled on a package worth around €55m, having been roughly €10m apart earlier in the week.
Bayern Munich's head of football Max Eberl and Eintracht Frankfurt's sporting director Markus Krosche have been in regular contact throughout the negotiations. The discussion now centres on how the fee is structured between a guaranteed amount and performance-related bonuses.
Frankfurt are pushing for a structure of €50m plus €5m in add-ons. Bayern, by contrast, want a lower fixed fee with a greater proportion paid through bonuses.
Brown, 22, signed for Frankfurt in January 2024 and has since become one of the most sought-after young defenders in the Bundesliga. He has already agreed personal terms with Bayern, with the move expected to be formalised once the clubs settle on the final structure of the fee.
There is a possibility Brown could undergo his medical for Bayern during the World Cup itself, allowing him to sign a long-term contract with the German champions before the tournament concludes.
His emergence has been one of the stories of the Bundesliga season, with Frankfurt having signed him from 1. FC Nurnberg for a fee in the region of €2.5m to €3m in January 2024.
Should the deal go through at the figures currently being discussed, it would represent one of the most significant returns on investment in recent Bundesliga history.
Brown's versatility, with the ability to play left-back, left-wing or right-back, fits the profile Bayern have been seeking as they assess their options at left-back beyond Alphonso Davies. For Frankfurt, a sale at this level would represent another example of the club's recruitment department identifying value that has gone on to be sold for many times the original outlay.
With personal terms already in place and the gap between the clubs narrowing, the main outstanding question now appears to be the precise mechanics of how the fee is paid rather than whether the transfer happens at all.