Keegan rejoined Newcastle four months ago and after a difficult start, successfully guided the Magpies away from the drop.
Newly appointed deputy chairman Derek Llambias, executive director of football Dennis Wise and vice-president of player recruitment Tony Jimenez were also at Friday's meeting.
The meeting was arranged after comments Keegan made following Monday's 2-0 defeat by Chelsea at St James' Park.
"Maybe the owner thinks we can bridge that gap - but we can't," said Keegan.
He went on to suggest that the Premier League is "in danger of becoming one of the most boring but great leagues in the world".
That prompted Premier League chief executive Richard Scudamore to respond: "I don't think anyone in their right mind seriously thinks it is boring."
BBC football correspondent Jonathan Legard said Keegan and the club needed "an air of stability and clarification".
He told Five Live: "Where does Kevin Keegan fit in because the worry around those among Kevin Keegan is that Dennis Wise is his successor in waiting.
"If it is going to be Dennis Wise choosing everything and Kevin Keegan is just meant to weave his magic and man-motivation, man-management and so on on the training ground, is that necessarily what he wants?"
A pre-match news conference ahead of Newcastle's final Premier League match of the season at Everton on Sunday was brought forward 24 hours to Thursday to pre-empt questions on the meeting with Ashley.
The 57-year-old Keegan, who rejoined Newcastle four months ago, said: "I know people might be disappointed by me saying we might not win the league, but there would be a real danger of me being whipped off to the nuthouse if I started saying that.
"There is a big gulf and it has been well documented, not just by myself but by many, many other people in the game whose opinions are respected."
He added: "I have seen what other people have come out and said, like Mr Scudamore, to defend or try to put a different slant on it, and I fully understand that.
"But what I expressed was my view, and I stick by it.
"The majority of people you talk to who have a knowledge of the game, they realise by looking back over the last six years that that top four has been the same."
Keegan, who turned Newcastle into title contenders when he managed them from February 1992 until January 1997, has been promised funds to attract big-name signings in the summer.
But he has repeatedly indicated his dissatisfaction that striker Michael Owen has not been tied down to a new contract, while he has also sarcastically said his relationship with his billionaire owner was good because they never spoke.
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