The 37-year-old former Roma captain was one of four members of Italy's staff who were infected during recent 2022 FIFA World Cup qualifiers, in an outbreak which has also hit eight players.
After a week, De Rossi's condition with a persistent fever and cough required more in-depth tests which revealed pneumonia, Gazzetta Dello Sport and Sky Sport reported.
The former Italy midfielder has as a precautionary measure been in hospital since Friday (AEST) at Rome's Spallanzani hospital which specialises in infectious diseases.
The Azzurri have suffered a wave of infections after their FIFA World Cup qualifiers against Northern Ireland, Bulgaria and Lithuania.
Players infected include Juventus pair Federico Bernardeschi and Leonardo Bonucci, Atalanta's Matteo Pessina, Paris Saint-Germain's Alessandro Florenzi and Marco Verratti, Freiburg's Vincenzo Grifo and Cagliari goalkeeper Alessio Cragno.
Several media reports suggested Torino goalkeeper Salvatore Sirigu has also caught the virus, but while the club has confirmed a case, it did not identify the player.
De Rossi joined the national team's coaching staff on 18 March as one of coach Roberto Mancini's technical collaborator until the end of this summer's delayed UEFA Euro 2020, which runs from 11 June to 12 July (AEST).
He spent 18 years at Roma before retiring in January 2020 after a few months in Argentina with Boca Juniors.
De Rossi played 117 times for the Azzurri between 2004 and 2017, winning the FIFA World Cup in 2006 and being part of the team which finished runner-up to Spain at UEFA Euro 2012.
He retired from international football after Italy failed to qualify for the 2018 FIFA World Cup by losing a play-off with Sweden in November 2017.
Having played in three FIFA World Cups and three European championships he is the fourth most capped Italy player after Gianluigi Buffon (176), Fabio Cannavaro (136) and Paolo Maldini (126).