Roberto Mancini has not ruled out the possibility of Daniele De Rossi still signing from Roma, with the Manchester City manager clear that he needs two or three more players if the club are to challenge for the Champions League.

The midfielder has declared he is staying at Roma but Mancini said: "I don't know this. It is difficult but I don't know what can happen. From my experience while the window is still open anything can still happen for every player."

Mancini, whose side travel to Liverpool on Sunday, admitted that a move for Swansea City's Scott Sinclair could still be possible and smiled when asked if Athletic Bilbao's Javi Martínez may arrive. He said: "It's difficult, his cost is too big."

Mancini also denied again trying to sign Liverpool's Daniel Agger – "There's no chance," he said – and retaining an interest in Chelsea's David Luiz. "I don't know. I read it in the newspaper but it's not true. I think he's a fantastic player but it's not true," he said.

Of those linked with moves away from the club, Mancini said Nigel De Jong "will stay here" and added: "Adam Johnson is a City player at the moment. We can't sell a player if we don't buy other players, because we won't have enough players."

Edin Dzeko is said to interest Juventus but Mancini said: "As for other players, we can't sell our players if we don't put other players in. We have 19 players and two or three players injured. It's impossible." Sergio Agüero, Micah Richards and Gareth Barry are all out.

While De Rossi, a midfielder who can play in central defence, may cost around £30m to prise away, Mancini is intent that City will add to their summer recruitment, which stands at only Jack Rodwell. Asked how many more players he needs to be competitive for the Premier League and Champions League, Mancini said: "The same we asked for when we won the championship in May. Maybe two or three more."

This summer Mancini has voiced his disquiet with Brian Marwood, the chief football operations officer, regarding the club's lack of signings. Of City's ability to sustain a challenge in the two competitions if he does not enhance his squad, Mancini said: "We have four competitions. The Carling Cup is not important like the Champions League but if we do a good job in the transfer market in the final week before the window closes we can have a team which has a good chance in that competition as well and reach the final.

"In January we will lose Yaya and Kolo [Touré] and Abdul Razak to the African Nations Cup and we could have a serious problem. For this reason I think we need to improve our team."

Mancini described as "ridiculous" the Fifa regulation that could allow Argentina to insist on flying Agüero to his homeland for a medical after he was named for the games against Paraguay and Peru next month. While Carlos Tevez, Agüero's club colleague has not been selected, the 23-year-old has, despite Mancini stating he will not be available until the Stoke City game on 15 September, at the earliest.

"No, its impossible," he said of Agüero's chances of playing for Argentina. "It's impossible because Sergio needs a minimum of two weeks without training and then after maybe he can start again. He can't go. If Sergio in one week can play, it's different, but at the moment I think he needs two weeks."

Argentina may still insist on conducting their medical assessment and that could mean him having to fly home. "He can go and after he can come back but – yes, it's ridiculous [if that happens]. These are the rules and we need to respect these rules. They are ridiculous rules but now we need to see what happens with Sergio in the next 10 days or two weeks and after we take a decision."

In Agüero's absence Mario Balotelli may make his first start in City's visit to Liverpool. "We have two days to decide this," said Mancini.

Balotelli was sent off in the corresponding fixture last season, having come on in the second half. He had a starring role as Italy's lead striker in their progress to the Euro 2012 final but Mancini denied it was important for him to be the focal point at City.

"The European Championship is like the World Cup," Mancini said. "One month, every player do 100%. But Mario is an important player also here and he can do better but I'm sure that he'll improve."