McAvennie played eight games for the Hammers at the start of 1987–88, failing to score, before he moved to Celtic for a then club record fee of £750,000 on 2 October 1987.[18] Graeme Souness had approached him to join rival club Rangers at the 1986 FIFA World Cup which would have made him the first Catholic player to play for the Protestant club, but he refused, being a supporter of Celtic.[19] He made his debut for Celtic the following day in a 1–1 draw at home against Hibernian.