Latics chairman Dave Whelan has identified Rosler as his No 1 target as he seeks a replacement for Owen Coyle who left the Championship club by mutual consent on Monday.
"We were given permission quite quickly by Brentford. They conducted themselves very well," Whelan said.
I've had a good look around and I've had very good reports on him. He's obviously former (Manchester) City and lives in the area. He's the type I'm looking for and I'm determined to get an agreement.
"I'm told he's mad keen to come and, I have to say, Brentford have been very good in their dealings. They are obviously reluctant to lose him but they've been very, very helpful.
"The aim would be for him to get us in the play-offs this year and get back up to the Premier League inside two seasons. I will tell him all of this when I speak to him but I hope we can get it done.
"I'm confident of landing him and hopeful that we can get this done and dusted on Friday morning. I'm not hanging around.
"Getting Uwe in is my sole intention at the moment. He is a good young manager whose progression I've followed closely.
"I don't really know the exact amount of compensation but would estimate at around £200,000."
Former Manchester City forward Rosler, 45, took charge of Brentford in June 2011 after previous managerial spells in Norway with Lillestrom, Viking and Molde.
The German guided the Bees into a ninth-placed finish in League One in his first season in charge and they narrowly missed out on promotion last term after losing to Doncaster in their final game and then going down to Yeovil in the play-off final.
Brentford have also made a good start to the current campaign and sit in fourth position after 19 matches.
Rosler has won a total of 60 matches as Brentford boss as well as drawing 40 and losing just 36 for a win rate of 44 per cent.
Wigan travel to Millwall for a Championship fixture on Saturday, while Brentford have an FA Cup second round tie at Carlisle on the same day.