But it happened, with great success, on the night of October 4, 1989.
It was the second leg of a League Cup second-round tie as Kenny Dalglish's side hosted Wigan Athletic.
When Ian Rush went off injured at half-time, Dalglish turned to Staunton and deployed the defender up front.
It proved a stroke of genius; the Republic of Ireland star responded by netting a hat-trick in front of the Kop as the Reds won 3-0 on the night and sealed an 8-2 aggregate victory.
"It was the second leg and we were 5-2 up from the first leg," Staunton told Liverpoolfc.com.
"Wigan asked to play the second leg again at Anfield so they could get the revenue from the gate receipts, and that suited us.
"I had played up front for Liverpool before. In pre-season we were in Norway and Kenny kept on trying me up front, so he had that in his mind.
"I suppose I didn't do myself any favours because when I was in the youth team at Liverpool I played up front once and scored a hat-trick!
"When Kenny asked me to play up front in the second half, he just told me to do what I did in pre-season, just go up top and make yourself available, and I was thinking, 'Thank God he didn't ask me to run the channels!'
"To get the hat-trick in front of the Kop, happy memories, my only senior hat-trick - so I was delighted.
"I've still got the match ball, all the lads signed it. I keep telling Rushie it was the best managerial decision Kenny ever took, taking Rushie off and putting me on because he never scored in that game, did he?"
The three goals came from finishes both Rush and Dalglish would have been proud of, the opener a beautiful touch into the net following a pinpoint David Burrows cross from the left flank.
"For the first one, all I did was make clean contact with the ball," said Staunton.
"As you know, Anfield - and even to this day - we always soak the pitch. It was greasy and once you make the contact with those Tango balls they just flew off and I was lucky to see it hit the target.
"That's what Kenny used to say to everyone, 'Try to hit the target and make the 'keeper work and you never know, you might score.'"
Staunton's second came after Molby was sent on to form an unfamiliar strike force, replacing the rested Peter Beardsley.
"Look at the creativity there, though. We ran them ragged and because we were that deep, nobody could pick us up!" he laughed.
"Look, Jan was an unbelievable player, just fantastic. He could pick a pass from anywhere. Whether that be from five to 10 yards or 70 yards, he could pick you out.
"He found me a couple of times and again, the second one, it was a nice strike and I just kept it low and hard, and luckily it went in the corner."
His hat-trick goal, meanwhile, was reminiscent of Rush or John Aldridge, as Staunton found himself in the right place at the right time.
He was able to capitalise on an open goal after a beautiful team move saw Steve McMahon draw out the Wigan goalkeeper and lay the ball into space.
"All the hard work was done and I just found myself in the middle of the penalty box on my own, no 'keeper, so a lovely little pass from Macca and I had the hard, envious task of tapping the ball into an empty net," said Staunton.
"Now and again fans will mention that to me to this very day but until the goals came up again recently on YouTube, people forget about that, and we have had better nights at Anfield with those big European nights.
"The Wigan game itself, we were through really after the first leg and not too many remember it, but I suppose the big thing is it's up on the wall in the Carlsberg Lounge at Anfield mentioning that hat-trick, so it's nice to be remembered."
Staunton was a proud member of the Dalglish team that produced some scintillating football with the likes of John Barnes, Beardsley, Aldridge and Ray Houghton purring in tandem together.
"If you look back, 1988, 1989 and 1990 it could have easily been three doubles for us, and it probably could and should have been," he reflected.
"It just wasn't meant to be, but that was an unbelievable team to play in.
"I probably got my chance because there were only two substitutes back then and I could play in numerous positions - or fill in, anyway!
"When you can play with good players like that, they can play in any position, and that is what we had at Liverpool."
In fact, such was his versatility, Staunton managed to feature in every position for Liverpool across two spells with the club - including as an emergency goalkeeper.
His brief foray between the sticks came in a Merseyside derby at Anfield in 1999 after Sander Westerveld was sent off.
"I did play in every position for Liverpool," he added.
"I was left-back, then played right-back, left centre-back, left wing, right wing, striker obviously against Wigan, and I also played a lot of games in central midfield, in goal against Everton and also plenty of times on the bench!
"It was just an honour and a privilege for me to play for such a great club."