Clarence Seedorf's men have won each of their last three league games and square up on Sunday against a side coming off the back of five successive Serie A defeats
The Sicilians sacked Rolando Maran for the second time this season on Monday after he had returned to replace his own successor, Luigi De Canio.
Maran's latest dismissal was prompted by a 2-1 home loss to Torino that left Catania seven points adrift of safety at the foot of Serie A.
Pellegrino, who previously led the club more than a decade ago and has been involved with the youth academy this season, now has the challenge of lifting a team that have suffered five straight defeats.
Catania have only won four league games all season but the new coach is determined to retain a sense of positivity.
"It's too early to give up and we have to give everything until the end of the campaign," said Pellegrino, who also played for the Rossazzurri. "On Sunday we're going to San Siro to challenge AC Milan and, as the coach of Catania, that is a source of pride for me."
Catania will certainly be underdogs when they come up against a Rossoneri team who have moved back into contention for European qualification in recent weeks.
Clarence Seedorf's men are 11th in Serie A but a run of three consecutive wins has seen them rise to within five points of city rivals Inter, who occupy fifth spot.
Despite Milan's welcome upturn in form, defender Philippe Mexes is adamant that he and his team-mates will not be taking Catania lightly.
"We went through a tough period but we're getting back now and we're on the right road," Mexes told the club's official website.
"The end of the season is very important for all of us and we can't afford to underestimate Catania. There are three important points up for grabs."
Milan are set to be without Keisuke Honda after the attacking midfielder twisted his left ankle in training.
The Japanese joins midfielders Michael Essien (thigh) and Sulley Muntari (calf) on the sidelines but long-term absentee Stephan El Shaarawy is nearing a return to the squad.
El Shaarawy has featured just four league games all season because of a foot injury and, although the meeting with Catania will come too soon for the Italy forward, he has now returned to training.