David Greenaway (20 December 1886 – 1946) was a Scottish footballer. Born in Coatbridge, Lanarkshire, Greenaway played junior football with Shettleston before being signed at the age of 19 by London club Woolwich Arsenal in the summer of 1908. Despite his youth he was immediately propelled into the first team, making his debut against Notts County on 2 September 1908, the first game of the 1908–09 First Division season. He only missed two games that season and went on established himself as a regular fixture on the wing for the following four seasons.