Sky Bet reported a "one-way flow of money" for the American, amid rumours that he was quitting his post as USA coach.
They were into 1/3 by lunchtime, Bradley having started the day as big as 4/1 with Paddy Power.
Sky Bet's Tim Reynolds said: "We've only laid one side to this market today so it looks as if people believe that Bradley will be named as the next Villa manager.
"He's now our worst result in the fieldbook so we'll be hoping that Randy Lerner looks elsewhere."
Other firms have also slashed their prices to odds-on, including bet365.
Their spokesman Steve Freeth said: "The reports about Bob Bradley quitting his USA post have been doing the rounds since Thursday night, but the crash in his price (3/1 into 4/7) suggests punters think he's going straight to Villa Park."
Bradley, who took the USA to the last 16 of this summer's World Cup, was the subject of an initial gamble on Monday in the hours after Martin O'Neill's resignation.
However, he drifted out in the following days as money came in for Sven-Goran Eriksson.
The Swede had drifted to 4/1 with Sky Bet by lunchtime.
