
The chances of Nunez rejoining the Reds, one year after being allowed to leave for Al-Hilal, appeared to gather pace this week.
A report from the striker's native Uruguay emphatically declared that a deal to bring him back to Anfield would be completed after the country's participation at this summer's World Cup ended.
But as the ECHO's Liverpool FC correspondent Paul Gorst explained in his latest Notebook, the report not only surprised club insiders, but also Nunez's camp, too.
That will please 2001 treble-winning hero Heskey, who addressed the rumours when questioned whether Liverpool need to bring in another centre-forward given Hugo Ekitike's serious injury.
He said: "It's kind of a short-term fix as opposed to being a long-term investment. I don't see that being the fix that we need if I'm honest.
"If he's terminated his contract (speculation suggests Nunez will), then we need to know why. I don't think it’s a good idea. I can't see that.
"With Ekitike's injury, it could be another six months at least. And the interesting thing with Liverpool that you always used to have, I've grown up in an era where we always had young lads that could come in and do your job for at least three or four months, if not the whole season.
"I'm the same. Well, I'm a little bit younger than Robbie Fowler but I saw him burst on the scene. I'm a little bit older than Michael Owen, and I’ve seen him burst on the scene. We've always had them, and where are we with these players now?
"And that's one of the things that Liverpool have probably got to look to tap into. But I can't see Darwin Nunez coming back - bad idea."
One player who has burst on to the scene is Rio Ngumoha. The 17-year-old was rewarded for a breakout season with the Reds by being called up to England's pre-World Cup training camp in the United States.
The winger won his first senior international cap and was named player of the match after being brought on at half-time in the 1-0 friendly win over New Zealand in Tampa.
And Heskey, who won 62 caps for England, scoring seven goals, said: "I think when you see some young lads coming through and you're really excited about them, what you're more excited about is the confidence, and he oozes confidence.
"To come on to the national team and to basically look like the best player out there at 17, is not easy at all. He's done that. He's come on on his debut, scored goals, come on and changed games, and he continues to impress every single time.
"Hopefully this season he'll be given more minutes to allow him to show exactly what Liverpool have been missing, which is a dynamic winger.
"Since Luiz Diaz, we haven't really had that dynamic winger who's going to get at defenders and cause them problems. The only thing with Rio is that the end product needs to be tightened up."
Should Ngumoha be granted more game time next season, that could spell bad news for Cody Gakpo.
The Netherlands international, who is currently competing at the World Cup, was one of the first names on the team-sheet for Arne Slot.
But with Slot now being replaced by Andoni Iraola, there has been speculation that Gakpo may look to leave, with Tottenham Hotspur and Bayern Munich two of the clubs who are said to be interested.
And Heskey, speaking to the ECHO via LiveFootballTickets, said: "I think Gakpo’s found it very difficult at times playing in England. It's not easy. He's found it tough.
"I'm not sure if left wing is his most natural position or is it No.9? We don't know as of yet. I don't see us getting the best out of him. So it’s probably a good thing for him to look for a move and try and get going again."