The nephew of Celtic great Johnny Madden, William Malloy was signed from Dumbarton Harp in October 1925.

The outside-right made his debut for the Bhoys in a 2-1 league win at Dundee on March 17th 1926 and scored a debut goal. Brought primarily as cover for Jimmy McGrory, Willie spent periods of his Celtic career on loan at Arthurlie and Ayr United. He played a total of eight first team games for Celtic before joining Dumbarton in September 1928.