Navas declared last week he was ready to leave Sevilla this summer.
And the 59-year-old Chilean could be joined on the plane to Manchester by winger Navas.
City's new director of football Txiki Begiristain has identified the Spain international as the club's top transfer target this summer, says Marca.
City could also try to poach his Sevilla team-mate Geoffrey Kondogbia. The 20-year-old French starlet has been tracked by the club's scouts for a number of months.