Without citing sources, the newspaper said Mousell, who is now managing director of automotive accessories chain Motor World, is discussing a transaction with two large investment banks.
But it said Mousell has received little encouragement from Boots.
The FT added that private equity bidders are also lining up offers for Halfords. It said these include Duke Street, Apax and Permira.
Mousell, 54, worked at Halfords for 22 years, leaving in 1992 to run a corporate entertainment business. He is now managing director of Motor World, the 200-store automotive accessories and bikes chain with annual sales of £55m.