William Hill said they had received more than 25 bets, each worth more than £1,000, in the last hour alone, on who the next Labour leader would be.
Paddy Power are offering odds of 4/6 on Mr Miliband with Schools Secretary Ed Balls, a close ally of Mr Brown, close behind.
Mr Balls is backed into 6/1 from 16/1, to be named new Labour leader.
Energy Secretary Ed Miliband, David's brother, is also a 6/1 contender to gain the Labour crown, according to Paddy Power.
They are also offering odds of 7/1 on Home Secretary Alan Johnson replacing Mr Brown.
Darren Haines, spokesman for Paddy Power, explained: "It would appear both Labour and Lib Dem figures are jostling for the removal of Brown and no doubt there will be deals to succeed him being made in the shadows of Westminster as we speak.
"The question now is who will be crowned Brown's successor and whether this happens sooner than the PM is hoping for."
William Hill have David Miliband as 4/7 odds on favourite, with Chancellor Alistair Darling at 8/1, Mr Johnson at 10/1 and Ed Miliband at 11/1.