Murray revealed he spoke to the former Manchester United boss - a long-time supporter of Murray - after his five-set win over Fernando Verdasco on Wednesday evening.
Sir Alex had been in the Royal Box and the conversation took place as Murray had treatment in the physio room.
"I spoke to him for 15 or 20 minutes after the match and we talked about a lot of things - about his retirement, about football and at the end I spoke to him not so much about the match but about everything that goes with it," said Murray.
"He was more just giving me some advice on how to handle certain pressures and expectations, that sort of thing. Getting that sort of advice from someone like him is gold dust, so I'm not going to be sharing much of it."