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Elliott was summoned from the bench in the 86th minute at the Parc des Princes in Wednesday night's round-of-16 tie and managed to make his mark just 47 seconds later by slotting past Gianluigi Donnarumma to seal a crucial 1-0 win for the Reds.
His goal secured the most unlikely of victories in the French capital after Arne Slot's side had managed just two shots on target and 30 per cent of possession over the 90 minutes of the first leg.
For the 21-year-old, it was the third consecutive Champions League game in which he scored, while he continues to find chances in the Premier League hard to come by.
However, Cole has called on the England Under-21 international to build on his remarkable cameo against the runaway Ligue 1 leaders as a springboard to force his way into Slot's Premier League plans.
Speaking to Paddy Power, the former Liverpool and Chelsea midfielder said: "I've always been a big fan of Harvey Elliott.
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"He's still a young pup, but he's got great ability when he comes inside on his right foot.
The Premier League is hard - and they must take their chances.
"Coming off the subs bench and scoring the winner against PSG would have been amazing for him.
And I'm really pleased for him because I think he's a top footballer."
Elliott's last Premier League start for Liverpool came prior to Slot's arrival at the club - May's 2-0 win over Wolverhampton Wanderers - with the midfielder limited to only 76 minutes across 10 outings this season.
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But the former Fulham youngster could be handed a first Premier League start of the campaign when Liverpool welcome Southampton to Anfield on Saturday afternoon.
Speaking in his pre-match press conference on Friday, Slot hinted that he could make a handful of changes for this weekend's Premier League clash as it is sandwiched between both games against PSG.
"If I make the choice to play other players, that is because I think that is the biggest chance to win the game tomorrow.
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