According to the Telegraph, the two full-backs are expected to make a switch to the Etihad in the next 48 hours. The Citizens are keen on wrapping up the signings of the two defenders as they look to bolster their defence for the new season.
Pep Guardiola already allowed three of his full-backs from last season - Pablo Zabaleta, Gael Clichy and Bacary Sagna - to leave the club this summer. In addition to this, Aleksandar Kolarov has asked the club to sanction his sale as he is set to join AS Roma on a £5.8m ($7.5m) deal.
Kyle Walker left Tottenham Hotspur and sealed a record move to City. The fee was believed to be in excess of £50m ($65m) as the England international became the most expensive defender. Despite his arrival, the former Barcelona and Bayern Munich manager has publicly expressed his desire to bring in "two to three" defenders in the ongoing window.
City need to strengthen their full-back position as they have already lost Dani Alves to Paris Saint-Germain. They need to step up their efforts in securing the deals for Danilo and Mendy.
The Telegraph report claims the Brazilian defender is expected to leave Real's UCLA training base in Los Angeles and join City's camp to undergo a medical. Guardiola and his men are also in the United States for the pre-season tour.
Real are set to pocket around £26.8m ($34.8m) from Danilo's sale to the Premier League outfit. He was a target for Chelsea, but the former FC Porto man has snubbed advances from the English champions in favour of joining City.
Meanwhile, Mendy has been heavily linked with a move to the Etihad. City have seen their multiple bids rejected by Monaco as they look to convince the Ligue 1 outfit to reduce their asking price for the left-back.
Monaco's resistance to let their player leave has forced City to prepare a fourth bid that is in excess of £50m for the France international. Guardiola's side remain confident that his side can complete both the deals for Danilo and Mendy before this weekend.
City have so far completed four signings and the list includes Mendy's former teammate Bernardo Silva, goalkeeper Ederson Moraes, Walker and Brazilian teenager Douglas Luiz. Should they complete double deals for Danilo and Mendy, they will take their summer spending spree to £217m ($282m) and is expected to reach £300m ($389.8m).