Italian journalist Fabrizio Romano reports that both clubs have agreed an €8 million fee with Gent and are battling to get the green light from the English defender.
While the Turkish giants appeared to be the front-runners, Milan are now trying to hijack the deal.
Both teams have reportedly arranged a private jet for Brown at the Brussels airport in their attempt to agree personal terms with the player.
Fenerbahce manager Jose Mourinho is keen on adding Brown to the squad, but the final decision rests with the talented left-back.
Milan are scouring the market for a left-back this summer after selling Theo Hernandez to Saudi Pro League giants Al Hilal for €35 million.
Manager Massimiliano Allegri wants a young and talented full-back in his project, identifying Brown as his desired target.
The 23-year-old has grown into one of the most promising full-backs in Europe, displaying excellent consistency at Gent.
Brown has netted three goals and 10 assists in 86 appearances for the Belgian club.
He also boasts eye-catching numbers, ranking in the 99th percentile for progressive carries, 88th for successful dribbles and 87th for through-balls.
Brown also excels in defensive actions, which makes him a well-rounded full-back who is effective in all phases.
Filling in Theo’s void would not be as easy as it looks due to his significant impact at Milan over the years.
The Frenchman’s under-lapping runs and a knack for spectacular goals make him a cut above the rest, and the Rossoneri will have their work cut out in finding his successor.
Brown has the quality and skillset to be a great investment for Milan, and his transfer fee is a bargain.