Shakhtar Donetsk midfielder Fernandinho was reportedly spotted in Manchester for a medical ahead of a rumoured £34 million move to the Etihad Stadium.
Signing the Brazilian would come soon after a deal for Sevilla winger Navas, which was confirmed, subject to a medical, by the Spanish club earlier in the week.
City, who are also believed to be close to appointing Manuel Pellegrini as manager, have not commented on either prospective transfer, but there are not believed to be any problems.
Both seem likely to be confirmed in the coming days along with the arrival of Pellegrini, who has been tying up loose ends after announcing his departure from Malaga.
It appears City intend to act decisively as chief executive Ferran Soriano and director of football Txiki Begiristain get their first full summer transfer window in which to operate in tandem since joining the club.
City’s failure to land any of their prime transfer targets last summer was regularly cited by former manager Roberto Mancini as one of the reasons for their regression last season.
The new manager may not yet be in place but City have made clear it will be Begiristain who drives their player recruitment policy.
City are thought to have been tracking Fernandinho, who shone against Chelsea in the Champions League last season, for some time and the 28-year-old has spoken of his desire to join the club.
His Shakhtar contract reportedly contained a £42.5million release clause but City may have been able to negotiate a compromise.
Spain World Cup-winner Navas is thought likely to cost City an initial £17m.
The 27-year-old has expressed excitement at his impending move, saying he is joining a “great club”.
City have also been strongly linked with Malaga playmaker Isco and he could follow Pellegrini to the Etihad Stadium.
Meanwhile, City and Arsenal will wrap up their pre-season programmes by taking each other on in a friendly in Helsinki.
The sides will play at the Olympic Stadium in the Finnish capital on August 10, one week before the new Barclays Premier League season begins.
The two clubs faced each other in a friendly in Beijing last summer.
Meanwhile, Richard Dunne was one of five Aston Villa players to be released by the club yesterday.
Dunne, 33, did not play last season due to injury and ended a year of misery by coming on for the final 25 minutes of Sunday’s 4-0 international friendly victory over Georgia — his first action since June last year.
The defender, who signed for Villa in 2009 from Manchester City, was hoping to use the end-of-season games with the Republic as a shop window in an attempt to find a new club and it remains to be seen if he is successful.
Elsewhere, Arsenal have confirmed Andrey Arshavin, Denilson and Sebastien Squillaci will leave the club on the expiry of their contracts this month.
All three were expected to depart the Emirates after dropping out of the first-team picture under manager Arsene Wenger.
Arshavin made 144 appearances, scoring 31 times. After a number of poor seasons he was eventually farmed out on loan back to Zenit at the end of the 2011/12 campaign. He was welcomed back into the Arsenal fold ahead of last season but went on to make just 11 appearances in all competitions for the north Londoners.
Brazilian midfielder Denilson, 25, leaves after 156 appearances for the Gunners between 2006 and 2011. He has spent the last two seasons on loan at Sao Paulo.
France defender Squillaci, 32, departs three years after joining from Sevilla, during which time he made just 23 league appearances.
Elsewhere, Fulham have signed goalkeeper Maarten Stekelenburg from Roma on a four-year deal.