The deal, which should be sealed by the year end, was worth about 500 million to 600 million euros, one of the sources said.
It follows a wave of deals in the European luxury hotels sector, including the purchase of Germany's Steigenberger hotels by China's Huazhu Group.
Varde bought a portfolio of nine hotels from Italian group Boscolo in 2017. It includes famous properties such as the Grand Hotel dei Dogi in Venice and Palazzo Naiadi in Rome.
Hotel investments are set for a record high this year in Italy, industry officials say. In the first nine months of 2019, investments in Italian hotels tripled to 2.56 billion euros compared with a year earlier, real estate services group CBRE said.
The head of Covivio's Italian arm Alexei Dal Pastro told a conference in Milan on Tuesday that Covivio was interested in investing in Italian hotels, without giving more details.
Covivio could not immediately be reached for comment on the Varde deal. Varde declined to comment.
French based Covivio has a stake of 42% in Covivio Hotels is specialised in the management and rental of real estate assets.
(This story corrects spelling in paragraph seven)
(Reporting by Elisa Anzolin; Editing by Silvia Aloisi and Edmund Blair)