The Barclays Premier League champions have had a quiet summer in the transfer market with Jack Rodwell, signed from Everton for a reported £15million, their only acquisition.
They continue to be linked with a number of other players before next week's deadline, including Swansea winger Scott Sinclair and Roma's Italy midfielder Daniele De Rossi.
Mancini, whose side travel to Anfield this weekend, said: "We have another week but I think today for us it is important to think about Liverpool.
"I am sure we will do what we want in one week.
"We are working, we can't say a name or how many players, but in the last days we will be working."
Another player reportedly of interest to Mancini is Athletic Bilbao midfielder or defender Javi Martinez but the City boss claims he is too expensive.
The Spaniard, also a rumoured target for Bayern Munich, is thought to have a £31million release clause in his contract.
Mancini, speaking at a press conference to preview the Liverpool fixture, said: "It is difficult, his cost is too big. It is too high for me.
"I repeat, we have another week, I think we will do something in this week but for me it is more important to think about Liverpool."
One player Mancini categorically claims he is not interested in is Chelsea defender David Luiz.
He said: "I read about it in a newspaper but it is not true. I think David Luiz is young and a fantastic player, but it is not true."
In terms of players leaving the Etihad Stadium, Mancini does not want to sanction any sales without having other players lined up.
Midfielder Nigel de Jong, who is now in the final season of his contract, is one whose future remains a subject of speculation and was recently linked with Inter Milan.
Mancini said: "I don't think Inter Milan want De Jong - De Jong stays here."
Winger Adam Johnson, who has struggled to command a regular place in the side, is another whose position is uncertain.
Mancini said: "Adam Johnson is a City player at the moment.
"We can't sell a player if we don't buy other players. If so we don't have the right number for this year."
Mancini also denied there had been any approaches for striker Edin Dzeko.
"No, not at the moment," he said.