Juventus have underperformed in Pirlo’s first season in charge of the club and face a battle to secure Champions League football for next season, with the Old Lady currently in fifth place on the league log.
Inter Milan’s 2-0 win over Crotone on Saturday means for the first time in nine years, Juventus will not be crowned champions of Italy.
The Bianconeri were also eliminated in the Champions League at the round of 16 stage by FC Porto, leading to reports that Allegri, who led the club to five straight Scudetto titles before stepping down in 2019, could return next season.
Under Pirlo, Juventus have won the Italian Super Cup in January and also have a Coppa Italia final date with Atalanta later this month.
"I'm fine," the 2006 World Cup winner said to reporters ahead of Sunday’s Serie A clash at Udinese. "I talked to the owners the other day. It's not the first time they've come. We had a little chat about everything, as we always do. I'm calm about my work.
"I read the names of possible successors from you. I don't allow myself to be influenced and I'm focused on what I have to do.
"We are aware that this is a very important moment: we have 15 points to win plus the Coppa Italia final. All matches are fundamental and we are focused on the next one.
"My goal is to win the remaining matches that will lead the team to the Champions League and win the Coppa Italia. I am not thinking about anything else: I'm calm and concentrated. These final days will be a fight to the end, with difficult matches for everyone... starting tomorrow."
Pirlo’s contract with Juventus expires in the summer of 2022.