Ranjit Boparan, owner of Harry Ramsden's restaurants, is set to buy Giraffe from Tesco.
Sky News reports the food tycoon's private investment vehicle Boparan Ventures, which also owns London-based chain Fishworks, is snapping up the restaurant chain for a "modest sum".
Boparan, whose known to be worth £1.35bn, is the founder of Britain's biggest chicken supplier 2 Sisters Food Group.
Tesco is also reportedly looking for buyers for Kipa, a Turkish grocery chain it acquired in 2003, as part of the retailer's plans to get rid of under- performing assets.
In April, Tesco partially offloaded its stake in ecommerce site Lazada to Chinese giant Alibaba.
The retailer's CEO Dave Lewis reportedly is looking for buyers for Harris + Hoole, the chain of coffee shops, and Dobbies, the garden centres business.