Bookmakers Paddy Power have installed the 36-year-old as the leading front-runner, ahead of the likes of Steve Cotterill and Ryan Giggs.
The Buckinghamshire club have been looking for a new permanent manager after Karl Robinson was sacked in late October.
The Dons held preliminary discussions with Steven Gerrard earlier this month, but the former England international turned down the offer, believing it was “too soon”.
Neilson took over at Tynecastle prior to the 2014/15 campaign. He led Hearts back to the Scottish Premiership at the first time of asking by winning the second tier crown ahead of Hibs and Rangers, and secured a top three finish last term.
However, he’s come under criticism from sections of the Hearts support, with supporters infamously paying for a plane to fly a “Neilson out” banner last season.