The report claims City are determined to land Suarez, with speculation continuing to link Sergio Aguero with Real Madrid.
The Argentinian international joined City from Atletico Madrid in 2011, but he has long been earmarked as a Real Madrid transfer target.
And the report claims City will move for Liverpool striker Suarez if Aguero does depart for the Spanish capital.
The reported offer is €40m plus Edin Dzeko, which would give the Anfield club a ready made replacement for the Uruguayan international.
But the Reds will be desperate to hold on to Suarez, who has become one of the best forwards in the world since his move from Ajax in 2011.
Despite missing the first five matches of the Premier League season due to his ban, Suarez is still the league's current top scorer with 14 goals.
Two better than City's Aguero, it's no surprise the two leading marksmen in the Premier League are being strongly linked with moves in the January window.