Endless is believed to have beaten rival bidder Better Capital, but has yet to sign a formal agreement, people close to the situation told Sky News.
A deal could be announced as soon as tomorrow, said the report.
Morrisons has said that it wanted to sell the business, which it bought for £70m in 2012.
In April this year Endless bought 35 outlets and the brand of West Cornwall Pasty Company, which had gone into administration.
That was the first deal from the firm’s Enact fund, which was launched earlier in 2014.
In March this year Endless made a return of six times from the sale of its stake in UK-based Acenta Steel to the company’s management.
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