Rangers remain managerless after the dismissal of Russell Martin last week. Liverpool legend Steven Gerrard was offered the chance to make a return for a second spell in charge, but pulled out of the running on Saturday.
Speaking on The Good, The Bad and The Football podcast, Scholes said: "I was actually with a lad the other night who told me he was actually going to meet Rangers.
“I’m not sure if he did but his name’s not been mentioned. I think he told me in confidence so I’m not going to tell you. I don’t think he was going for it.
"They contacted him and he was going to meet him in London the day after.”
Former United teammate Nicky Butt said: “(It’s) Ole (Gunnar Solskjaer) you’re talking about, aren’t you?”
Scholes then replied: “No, no comment.”
Solskjaer is available after his dismissal by Besiktas last month.