Having spent his entire managerial career in Italy and now at the age of 66, Gasperini has rarely been linked with a move to a European giant in recent times.
However, that has changed over the past week on the back of his Atalanta side comprehensively overcoming Liverpool by a 3-0 scoreline at Anfield.
That has put the Serie A outfit in a commanding position ahead of the second leg of their Europa League quarter-final fixture, which takes place on Thursday night.
Gasperini is on the verge of leading La Dea to a first-ever appearance in a European semi-final in a role that he has held since 2016.
Gasperini "happy" with Liverpool links
Given the magnitude of the game to be played at the Gewiss Stadium, Gasperini is naturally keen to focus all his efforts on that fixture.
Nevertheless, at his pre-match press conference on Wednesday, the veteran manager was quizzed on the recent speculation, acknowledging that he is enjoying being held in the conversation to be Klopp's replacement.
Speaking to reporters, Gasperini said: "Of course I am happy with links to Liverpool job to replace Klopp but my focus is on the game.
"We can't be distracted by this kind of links or stories, we have to focus on the upcoming games."
On the encounter itself, he added: "We are happy to play a match of good quality in front of our fans. This value, finally with the stadium taking shape. We know that it will be one of the most important matches in history, if not the most important.
"But these are things that are said on the eve of the match, then the moment comes when we will have to know how to isolate ourselves. We must, knowing that the result is what counts."
Is Gasperini a realistic target for Liverpool?
If Atalanta win the Europa League or claim a top-four spot in the Serie A table, it will not come as a surprise if Gasperini is linked with more clubs other than Liverpool.
Atalanta possess the third-best attacking record in the Italian top flight, scoring 57 goals from 31 games, and only trail the two Milan clubs on that front.
Nevertheless, everything points to Gasperini only being a backup contender for Liverpool with Sporting Lisbon's Ruben Amorim remaining the odds-on favourite.
The Portuguese is in a similar position to Gasperini in the sense that he wants to focus on winning at least one trophy with his current club before the end of the campaign.
Brighton & Hove Albion's Roberto De Zerbi remains as the second favourite, despite reports that he has recently dropped down the pecking order of potential successors to Klopp.