The Mirror reports that City’s bid is an increase on the £47million bid they tabled on Monday.
Wolfsburg are expected to reject this latest bid from City as they are holding out for £57million for the highly-rated winger.
City are reportedly prepared to offer the 24-year-old a six-year deal worth more than £200,000-a-week.
City boss Manuel Pellegrini is desperate to bring in the winger before the transfer window closes.
De Bruyne joined Wolfsburg in a £18million deal from Chelsea in January last year.