Although born in Scotland, Reeves spent his entire playing career in England and Wales.
He was invited to trials at Chester in 1961, making his debut in The Football League for the club against Rochdale in October 1963.
On 9 January 1965, he made a superb one-handed save at Old Trafford to deny Bobby Charlton in Chester's 2-1 defeat against Manchester United in the FA Cup third round.
[1] Reeves asked Chester for a transfer after losing his place to Terry Carling during the 1966–67 season.
[1][2] Reeves felt he produced the best form of his career playing at Wigan's Springfield Park,[1] which included the 1973 final of the FA Trophy at Wembley Stadium.