Storehouse, which owns Mothercare, is tipped as the most likely buyer of the chain, which is expected to fetch around pounds 40m-pounds 50m.
Boots declined to comment on the possible sale yesterday. Storehouse also declined to be drawn on details, but a spokesman said Mothercare's first out-of-town store, which opened in Fosse Park, Leicestershire, last year, had been a success. All 52 branches of Childrens World are out of town.
Boots has been under pressure to take the axe to some of its under-performing business, which include the DIY chain Do It All as well as Fads and Homestyle.
Boots started Childrens World in 1987, hoping to capitalise on a demand for hassle-free shopping for children that involved an element of fun. The stores sell toys, clothes and nursery equipment and feature play areas which include helter-skelters.
However, the concept struggled to take off and the chain has never made a profit. Last year losses increased to pounds 1.9m on sales of pounds 50m. Christmas trading was also poor, with the company blaming aggressive price competition on toys.
The sale would be welcomed in the City, which feels the success of Boots the Chemist is being held back by losses in other areas.
Tony Shiret, retail analyst at BZW, said: "There is logic to the deal. It would give more scale to Mothercare and it would have greater buying power than Boots. Childrens World is a bit of an irrelevance to Boots and if they sold it, it would show a determination to get rid of some of the other under-performing businesses."
Storehouse would be expected to change the store names to Mothercare, which already has more than 260 branches, and derive other benefits from economies of scale.
Mothercare has been a star performer for Storehouse. Its profits jumped by 120 per cent to pounds 9.3m in the six months to October. However, Christmas trading was disappointing, with management blaming a difficult market. Storehouse shares closed down 1p at 293p.