It comes after Falcao, the 26-year-old Colombian, is expected to leave Atletico Madrid at the end of this season.
Mancini flew to Madrid to speak to Jorge Mendes, and more than one meeting has taken place, which suggests City are pushing hard to outmanoeuvre Chelsea and Real Madrid, The Telegraph reports.
According to the paper, Falcao wants a 6 million dollar salary after tax, which means around double that in gross terms, so the full cost would be around 85 million pounds.
Mendes also represents Real coach Jose Mourinho, which has made that club favourite to sign the striker, while he has also kept strong links with Chelsea, the paper said.
However, Chelsea could only acquire Falcao should they sell Fernando Torres and may concentrate on signing younger attacking players such as Bayer Leverkusen's Andre Scherrle, it added. (ANI )