Mr Monk, who lives near Bolton Abbey, started work for the club when he was 15 and used to work half a day as a groundsman and train for the other half, until he reached 17.
He played as an inside forward in United's 1954-1955 intermediate team. They went through the entire season unbeaten.
Brian was at the club from 1953-58 and regularly played snooker with the late, great John Charles.
He recalled: "I was a better snooker player than him but he always won. We played for a few bob and he would always ask me if I could afford it and I would say, 'yes'. When it came time to go home, of course, I had no bus fare and I used to walk home from Elland Road to East Leeds in the winter!"
He added: "I am in the process of planning a reunion, but there are still some players we need to find.
"If anyone has information on Mick Shelton, who might live in Normanton, or Peter Grundy, from Leeds, then we would like to hear from them."
Mr Monk can be contacted on (01756) 711145.