As revealed by Goal in June, City were among a number of clubs to have made an enquiry regarding the Brazilian earlier this year, but were told the player had no desire to leave the Santiago Bernabeu.
City established Kyle Walker and Dani Alves as their top right-back targets after that, only for Alves to perform a shock u-turn and back out of his agreement with the club to join Paris Saint-Germain, forcing them to reassess their options.
Reports in Italy have suggested that City have agreed a deal for Danilo, though Guardiola was unwilling to shine too much light on the progress of the deal.
"We have many options for players who are coming, but Danilo is not done so until it is done I cannot say absolutely anything out of respect for other clubs, but he is an option that we have," Guardiola told a press conference.
"I said he’s a player from Real Madrid, we are talking with not too much players, with three or four players to come and join us. Not just for next season but the next three, four, five years, because they are all young players."
Danilo's situation at Madrid also changed while City pursued Alves.
The 26-year-old had his head turned by serious interest from Juventus throughout June and was ready to make the move, but the Italian champions could only sign one non-EU player this summer and after agreeing terms with both Danilo and Bayern Munich's Douglas Costa, they elected to sign the latter.
Chelsea are also reported to have shown an interest in the right-back but City are now hopeful of securing his signature by the time they fly to Los Angeles on Friday.
Reports in Italy claim a deal worth as much as €35 million has been agreed with Madrid.
City are in the United States for the International Champions Cup and after meeting Manchester United in Houston they will travel to LA to play Madrid, Danilo's current club.
Madrid are currently training in LA, which would help smooth the final stages of the deal.
City boss Pep Guardiola has been an admirer of Danilo since coming up against the Brazilian while in charge of Bayern Munich.
Should Danilo join City in the next week, he could make his debut against his former club. City signed Walker from Tottenham for £45m last week, meaning he will also face his former club in Nashville.