The Blues finished third in the league last season, nine points behind champions and bitter rivals Manchester United.
"We want to improve on last season and we'll try to win the Premier League but we need two or three more players and, if we can do that, I think we will be very close," said Mancini.
"But look at United – they have 29 senior players whereas we have 20. To be competitive, we need more.
"We're missing players, we don't have enough for the whole season and it's a problem. We haven't managed to get all the players we want and it is important we get them now in the next seven days."