Latics are searching for a new manager for the second time in six months after parting ways with Owen Coyle on Sunday night, when the ex-Burnley and Bolton boss' offer to resign was accepted by Whelan following three successive home defeats.
Out-of-work Ian Holloway, who has twice won promotion out of the Championship with Blackpool and Crystal Palace, was the first to publicly declare his interest in the vacancy on Tuesday night but it appears Whelan has set his sights firmly on Rosler.
And a deal could be concluded by Friday ahead of Wigan's visit to Millwall this weekend.
"We have permission to talk and I will be meeting him and hope to get it done tomorrow (Friday)," Whelan told BBC Sport.
The former Manchester City striker retains family ties in the north west and plays an attacking, pressing style of football which both Whelan and Latics supporters demand after Roberto Martinez brought them an FA Cup with similar tactics last May.
Rosler has been with the Bees since 2011 and his side would have been joining Wigan in the Championship this term had Marcello Trotta's last-gasp penalty been converted rather than hitting the crossbar in their famous end-of-season clash with Doncaster last term.
They came close to achieving promotion with a second bite of the cherry too but lost to Yeovil at Wembley in the League One play-off final.
However, the 45-year-old German, who had spells in charge of Norwegian clubs Lillestrom, Viking and Molde before joining Brentford, may get a chance to manage in the Championship this season after all.
Whelan added: "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 tomorrow."
Rosler is unlikely to come cheap, though, after penning terms on a new deal in January which expires at the end of the 2014-15 season.
The compensation package is unlikely to deter Whelan too much given the parachute payments and the increased revenue which this term's Europa League campaign has brought to Wigan.
Whelan is keen to have a new manager at the helm quickly, with an instant return to the Barclays Premier League still a distinct possibility.
Following Wednesday night's defeat to Leeds, Latics are 14th in the table, nine points off the play-off spots, while they remain in the hunt for the last 32 of the Europa League ahead of Thursday's concluding round of fixtures.
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