The deal comprises over 300 Booze Buster and Wine Cellar stores. Cellar 5's Right Choice c-stores have been sold to several buyers including Bargain Booze, A&S Stores and Spar wholesaler AF Blakemore.
A First Quench spokeswoman said: "We were not able to reach agreement on valuations. Having turned this business around over the past two years, we have not come this far only to overpay for distressed assets."
Maryland declined to comment on its plans for the chain.