The former United captain has not worked as a manager since leaving Ipswich in 2011.
He has been linked to several roles since including a return to Sunderland, who he guided to the Premier League before stepping down.
Keane, 52, revealed he once interviewed for the West Brom job with Ashworth, who spent time at the Baggies when they were a Premier League team between 2007-12.
However he was turned down by the man who became United's sporting director earlier this month.
Keane joked as he spoke about Ashworth's arrival at Old Trafford on the Stick to Football podcast.
He said as cited by Sports Central: “I don’t know if he’s that clever because he interviewed me for a job a few years ago and didn’t give it to me. It was the West Brom job. “The interview was good, just a bit of chit chat about football and my plans. It’s always strange for any manager, what is a good or bad interview? It’s hard to gauge. “Sometimes you get a feeling for somebody, and you respect who they go with. I sat with him, and it wasn’t meant to be obviously.”
The Red Devils first agreed terms with Ashworth last year but were made to wait to bring him in.
That is because his previous club Newcastle demanded a huge compensation fee.
The 53-year-old was then placed on gardening leave by the Magpies more than four months ago following interest from United.
But the two clubs finally agreed a compensation package following reports Newcastle wanted £20m for the transfer guru.
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