In 2014, City spent £32m to sign Mangala from Porto but, although the centre-back has made 79 appearances in all competitions, the transfer has not proven to be a success.
Mangala made an impact on loan at Valencia last season, but it was not enough to earn himself another chance under Pep Guardiola and the 27-year-old will be available on a free transfer in the summer.
According to The Sun, Wolves are ready to make their move and are prepared to meet Mangala's wage demands due to not being required to pay a fee for his signature.
Mangala is currently sidelined by a serious knee injury sustained in just his second game on loan at Everton, but that is unlikely to stop Wolves from trying to push through a deal.
The player is represented by super-agent Jorge Mendes, who played a role in Fosun International's successful takeover of the Championship winners.