Sky Deutschland are among the outlets in Germany who are reporting that a fee of 74m euros for the attacking midfielder has been “agreed in principle”.
Manchester City themselves are currently declining to comment on the reports.
But De Bruyne’s agent Patrick de Koster said: “There is no final agreement with Manchester City, maybe there will be tomorrow.”
Formerly with Chelsea, Belgium international De Bruyne has been a big success at Wolfsburg since they signed him in January 2014, breaking the Bundesliga record for assists last season.
In June De Bruyne revealed that his agent had been in informal contact with City representatives over a possible move to the Etihad.
City reportedly had a £47m bid for the 24-year-old turned down earlier this month but talks over a deal intensified late last week.
Wolfsburg are believed to have agreed to let De Bruyne move to the Premier League for a fee which could end up in the region of £58m with add-ons.
Manchester City have been very active in the transfer market this summer as they look to regain their Premier League title, Raheem Sterling, Nicolas Otamendi and Fabian Delph headlining their list of acquisitions.