The news comes just weeks after DM Private Equity, of which Cook is chairman, put the chain into administration.
Rival chain Thresher has taken on 200 former Unwins stores but Cook is believed to have submitted an offer for some or all of the remaining 181 outlets.
It is not clear whether this bid is through DM Private Equity or a separate investment source.
He is likely to face competition from other parties believed to be keen on snapping up some of the Unwins estate. These include wholesaler Whittalls Wines and Wine Cellar.
For further details on Unwins read this week’s issue of The Grocer