Mourinho was sacked as manager on Tuesday after a two-and-a-half-year spell in charge.
His departure followed Sunday's 3-1 loss to AC Milan, another low in a season disrupted by injuries and marked by poor results that have left them ninth in the table, 22 points behind leaders Inter Milan.
De Rossi, who has a contract until the end of the season, has only had one previous job as a manager, a brief spell in charge of SPAL in Serie B during the 2022-23 season.
"I haven't coached in a while, but they say it is like riding a bike. Even though I only coached for a few months, it was simple enough," De Rossi said.
"I am convinced that the team and I don't need any parachutes. This is a strong squad with some very important players."
Verona should be beatable opponents, having won only four of their 20 games this season to sit 18th in the standings.
There are just six matches this weekend as Napoli, Fiorentina, Inter, and Lazio are in Super Cup action in Saudi Arabia.
Juventus will travel to Lecce on Sunday looking to extend a six-match winning streak in all competitions and a 15-match unbeaten league run.
Victory will put them above Inter at the top of the table, with the two sides involved in a cat-and-mouse battle for Serie A supremacy.
Milan manager Stefano Pioli has earned some breathing space after their victory over Roma following some disappointing results earlier in the season. He is not, however, completely out of the woods yet.
Third-placed Milan visit Udinese on Saturday.
While Udinese are languishing in 16th they have sprung some surprises, having secured a 3-0 victory over Bologna in December and winning their last two league matches against Milan.
Pioli's side continue to grapple with a lengthy list of absences with defenders Malick Thiaw, Fikayo Tomori, Alessandro Florenzi, Mattia Caldara and Pierre Kalulu all injured.
