The club's former boss, who was in charge between 2006 and 2008, has been linked with the vacant role in the North East, after Lee Johnson was sacked earlier this week.
And the ex-Premier League hard man recently recalled a story of when he was managing them in the top-flight and tried to sign Taylor, as they looked to avoid relegation.
The former West Ham midfielder was surplus to requirements at Portsmouth and had a choice of moving to the Black Cats or Bolton.
But Keane couldn't believe the way that Taylor turned down a move to the Stadium of Light - texting him before he'd even left the club's car park!
"Trying to get players up to Sunderland is always difficult; their wives didn't want to go up there because they wanted to go shopping," the former Manchester United man told Off The Ball.
"Eventually, I got Matty Taylor up as he was leaving Portsmouth and had the opportunity to go to Sunderland or Bolton.
"So I met him at the stadium, in the boardroom, gave him all the talk for an hour or two… he said he's got a lot to think about.
"I said: 'Of course, you take your time, it's a huge decision. I'll walk you down to the car park'. As we walked down he says, 'listen Roy, it's a huge decision, thanks for the chat'.
"Bolton and Sunderland… there is no comparison, but listen, Bolton weren't a bad team at the time.
"I saw him walking to his car and say, 'brilliant, thanks for coming'.
"He turns his back and I've got a text, and not many people text me.
"It says, 'Hi Roy, it's Matty Taylor…'
"I've got my phone; I think it was a BlackBerry, at the time they were in. I can see him getting into his car!
"[The message continued] 'I've decided to go to Bolton'. And I'm there waving him out the car park!"
If he gets the job, let's hope Keane has more luck signing players during his second spell at the club.
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