Raggi, who was elected on Sunday, said during the campaign that she did not regard the bid as a priority for the cash-strapped capital.
But with the attempt to secure the Games strongly backed by Prime Minister Matteo Renzi, she has stopped short of saying she will withdraw City Hall support for it.
"The fact we are dealing with a new person in charge of the City does not change our plans," Malago said Tuesday on a visit to Juventus's new medical facilities, the Gazzetta dello Sport website reported.
"Ask her what she intends doing. Me, I'm simply inviting her to be loyal and collaborate."
Raggi won Sunday's election with over two thirds of the votes cast on the ticket of the populist Five Star Movement.
Her comments about the Olympic bid have been attacked by rival politicians as undermining Rome's chances in its battle with Budapest, Los Angeles and Paris.