The former Manchester United manager appeared to exclaim “That was good!” as he watched Murray seal a straight sets victory over Kevin Anderson on Centre Court last night.
The two Scots then got together after the match to discuss how to succeed in close matches.
Murray said: “He just said a few things, what he’s observed when he’s been watching me, not necessarily about technical or tactical things, but more sort of mental things, how you respond to tough or tight situations.
“Obviously you’re going to listen to someone like him. He’s witnessed a lot of big sort of tight sporting occasions. He obviously knows his stuff.”
Murray said he is in contact with Sir Alex “throughout the year” but denied the ex-manager could join his support team.
“He’s someone I would obviously talk to if something came up that I felt I could benefit from speaking to him about something. But I wouldn’t see myself employing him or offering him a job within my team. I wouldn’t see that happening.”
Rafael Nadal, Roger Federer and Maria Sharapova are among the stars in action today.
Murray faces a quarter-final clash with Grigor Dimitrov tomorrow.
The wet weather disrupted the tennis yesterday, causing the Centre Court roof to be closed and holding up play on the outside courts.
But forecasters at the Met Office predict today will be dry with sunny spells and light winds with a maximum temperature of 21C (69.8F).
Meanwhile a cyber row appears to have broken out between British tennis supporters.
The area where fans at the All England Club watch Wimbledon on a giant screen was originally labelled as Henman Hill on Google Maps.
It was renamed Murray Mound after Andy Murray won his title last year, but it was changed back - possibly by a disgruntled Tim Henman fan - during the last two days.
A spokesman for Google said the changes are being made by users of Map Maker, a tool where people can add places to Google Maps.