The 24-year-old has attracted attention from top clubs around Europe with his performances in Ligue 1 last season, helping Christophe Galtier's side finish second in the final standings.
The Ivorian contributed an impressive 23 goals and 11 assists in 41 domestic outings for Lille, emerging as one of the most consistent performers in France.
Pepe admitted back in March that he is unsure where his future lies, with the likes of Barcelona, Arsenal and Bayern Munich keeping a close eye on his situation.
Liverpool have also reportedly identified the Lille star as a summer target, but no formal offers have been submitted as of yet.
Nicol, who was part of the legendary Reds squad which dominated English football throughout the 1980s, has advised Klopp against making a move for Pepe.
"I really don't get this one," Nicols told ESPN. "Yes, he's had a good season but he just doesn't look like a Liverpool player to me.
"He's a little unorthodox, he looks gangly. He has got it done, the stats bear that out.
"Unfortunately it is Ligue 1 and I'm not a huge fan of Ligue 1, I don't think the standard is particularly great.
"Before the season kicks off we know PSG have won the league. I'm not sure of this.
"I'm not sure where it's coming from, to be honest, but I don't think this guy fits in with Liverpool."
Liverpool are not expected to make major changes while the transfer window is open, after winning a sixth Champions League and finishing as runners up in the Premier League last season.
However, Daniel Sturridge and Alberto Moreno's services will not be retained for the 2019-20 campaign, while back-up goalkeeper Simon Mignolet and long-term loanee Marko Grujic have been heavily linked with permanent moves.
There has been some suggestion that Liverpool have only been linked to Pepe in order to drive up his price, with Lille's current valuation of a prized asset set at around £60 million ($76m).