At the time of Chris Huhne’s resignation the Lib Dem odds stood at 6/4 but have been brought down to 4/9.
William Hill also reported that Lib Dem candidate Mike Thornton has attracted 28% of all bets so far struck.
The Conservatives were the original favourites, at 1/ 2, but their odds have drifted out to 2/1 second favourites - 21% of all bets struck have been for them.
“The Lib Dems are ahead in the betting and in the number of bets struck, so it will be a shock in betting terms if they fail to win,” a William Hill spokesman said.
Labour, whose candidate is comedian and author John O’Farrell, is on 16/1, having opened at 100/1, and they have been the subject of 27% of all bets struck, with UKIP attracting 20% of bets and currently offered at 25/1, having opened at 100/1.
National Health Action are 80/1 to win and have attracted 2% of bets struck.
Voters will go to the polls in Eastleigh next Thursday. The candidates are:
Conservative - Maria Hutchings
Labour - John O'Farrell
Liberal Democrats - Mike Thornton
UK Independence Party - Diane James
National Health Action - Iain MacLennan
Peace Party - Jim Duggan
Independent - Danny Stupple
English Democrats - Mike Walters
Monster Raving Loony Party - Alan Hope
Wessex Regionalists - Colin Bex
Elvis Loves Pets - David Bishop
The Beer, Baccy and Crumpet Party - Ray Hall
Christian Party - Kevin Milburn
Trade Unionists and Socialists - Daz Procter