The group is understood to have approached several potential buyers in the off-licence industry about the sale the business, according to informed sources.
However its initial approaches have been rebuffed and it may find it difficult to find a buyer, raising the possibility of an eventual management buy out.
Oddbins was put up for sale last spring with a price tag of up to pounds 50m. Tesco and Greenalls were in the frame to buy the business back but balked at the cost after having a closer look at the deal.
The chain was eventually taken off the market. However Seagram is still keen to offload the business and has made it clear it is open to offers.
The price tag demanded is believed to have fallen to pounds 35m, although some City observers believe that it may fail to fetch that much and could go for nearer pounds 25m. Analysts believe that buyers have been put off by fact that Oddbins sites are mainly leasehold which attract relatively high rents. Some of its sites are also considered too small.
Founded in 1963, Oddbins now has 238 stores in the UK. Its sites are concentrated in around London and the South-east, although they stretch from Inverness to Truro and it recently opened two shops in Dublin. But it is a minnow compared with Thresher and Victoria Wine.
The disposal would herald the latest step in the rationalisation of an industry that has been battered by intense competition from the supermarkets, which have managed to undercut off-licences and win market share.
The flood of cheap duty-free imports from the Continent has also hit sales. Greenalls sold its Cellars off-licence business last year and sources suggest Whitbread is looking to sell the Thresher chain. A spokeswoman for Seagram declined to comment on the fate of Oddbins.