Udinese's Chile forward Alexis Sanchez
It said City executives were due to fly out to Italy on Monday and were ready to improve an offer of £22.1 million ($35.8 million) for the 22-year-old which has already been turned down by the Serie A side.
The paper added City might have to go as high as £34 million to sign the striker.
Sanchez impressed at last year's World Cup and followed up by scoring 12 league goals as Udinese qualified for the Champions League.
City won this season's English FA Cup—their first major trophy in 35 years—and finished third in the lucrative Premier League, both achievements coming under the guidance of Italian manager Roberto Mancini.
City's Abu Dhabi based owners are reckoned to have lavished £300 million ($487 million) on signing players since taking over the north-west club in 2008.