Pirlo has been ruled out of the Euro 2016 Group H qualifier at the Stadion Vasil Levski due to a calf injury, while Daniele De Rossi is also unavailable for the same reason.
Italy coach Antonio Conte has urged Verratti to "take the reins" in Sofia and the Paris Saint-Germain midfielder has vowed to take his chance.
He said: "I can take control in midfield and help to dictate the game, but only if I have the support of the rest of the squad. If you aren't as talented as (Lionel) Messi or (Diego) Maradona, you have to rely on your team-mates.
"If I get the nod for either of the games, I hope to be able to grasp my chance. It would be great if I could symbolise the generation change because that would mean I'm doing well and the team counts on me. When Pirlo is available, it's only normal that he plays.
"He is a champion and has won everything, while I still have to fight to earn my place in the squad. Perhaps the coach will let us play together in the future. I'm more than prepared to play in different positions, like I've done in the past.
"I don't mind being charged with responsibility. Every time you pull on the national shirt, you have to try to put in a solid performance and not make any mistakes. It will be a tough game against Bulgaria, which we need to approach in the right way. I don't feel under pressure; I will give my all and try to do my best."
Italy are joint top of the group with Croatia after drawing 1-1 with Niko Kovac's side in their last qualifier back last November.
There are some new faces in Conte's squad and the Italy coach has been criticised in some quarters after picking two players born outside Italy in the form of Sampdoria striker Eder and Palermo midfielder Franco Vazquez.
Empoli midfielder Mirko Valdifiori has also been given his first international call-up for the game against Bulgaria and the friendly with England next Tuesday.
New Bulgaria coach Petev faces a baptism of fire in his first competitive game since taking over as Luboslav Penev at the start of the year.
Former Ludogorets boss Petev takes over a side sitting fourth in the group with only one victory from their first four qualifiers.
The 39-year-old was forced to make two late changes to his squad, with Levski Sofia defender Borislav Stoyche and Slavia Sofia forward Radoslav Vasilev replacing injured twin brothers Iliya and Georgi Milanov.
Petev said: "We should do our best. We must stay calm and avoid elementary mistakes. Italy are very strong side and we need the total support of the fans."