But 19-goal top scorer Tévez will be in Buenos Aires when Man City kick-off a game crucial to their Champions League aspirations after being granted permission to return to Argentina following the birth of daughter Katie, who was born six weeks prematurely last Monday.
Related ArticlesManchester City v Liverpool: previewMancini denies rift with BellamyVieira rejects ban challengeMan City open contract talks with JohnsonCity swoop for Ben HaimSport on televisionAlthough Mancini is keen for the £25 million forward to return to England in time for next Sunday's trip to Chelsea, if not Wednesday's FA Cup fifth-round replay at Stoke, the City manager is reluctant to impose a deadline on the 26 year-old.
But with preparations for the Liverpool game disrupted by the Bellamy saga, plus Patrick Vieira's three-match ban for violent conduct, Mancini insists that his biggest concern revolves around Tévez rather than Bellamy.
Mancini said: "I am frustrated because we don't have Carlos here. The other things are normal in a football team. It can happen, if not every day, then every week or every 10 days.Sometimes it is in the newspapers, sometimes not, but it's not a serious problem.
"Carlos is a serious problem because he can't play on Sunday and didn't play against Stoke two times in the last week.
"I hope Carlos comes back very quickly because we need him. I didn't ask him what the problem is but he wants to stay in Argentina, near his family.
"This is a difficult situation. There have been some problems with the baby because it was born early.
"I hope only that Carlos can solve his problems with his family and come back very quickly. I told him we need him and we have important games."
The absence of Tévez, combined with Vieira's suspension and a knee injury that will sideline winger Martin Petrov for four weeks, has placed an air of crisis over City ahead of the Liverpool fixture.
But Mancini insists that Bellamy, if fit, will be considered against his former club after insisting that the pair had resolved their differences over the 30 year-old's training regime, which necessitates the Welsh forward tailoring his physical work to avoid exacerbating a knee problem.
Mancini said: "I read that I have a problem with Craig and I read that I shouted at him. I have spoken with him face to face, manager to player, but I never shouted at him and I did not send him away for three months.
"The discussion with Craig was about the injury, the problem with his knee. He worked one way, I preferred another way.
"I prefer him to work with the fitness coach, he prefers to work another way, but it is resolved and I am happy with the way it is resolved.
"I have spoken with him in my office, but these are normal things. I have worked with big players, players who have won the Champions League and the World Cup, and his temperament is not a problem."
Victory against fifth-placed Liverpool would lift City four points clear of Rafael Benítez's team, who have played one game more.
League games against Chelsea and Tottenham follow for City and Mancini admitted they were crucial to his team's ambitions.
He said: "After those three games we have another 10. If we lost the three games, it could be difficult to finish fourth but we haven't lost the three games.
"Now we must think about Liverpool because it is the first game and it is important that Carlos comes back."
Javier Mascherano, a close friend of Tévez and the striker's former team-mate at West Ham, acknowledged that the Argentine's absence was good news for Liverpool, but admitted his primary concern remained his friend's family. "That is the main thing," said Mascherano.
"I was worried because the baby was born before the due date and it was difficult for him. The most important thing is that he is happy and the baby is well."
The Argentina captain, though, was less conciliatory about Tevez's club side.
City were linked with a move for the Liverpool midfielder last summer and are expected to rival Barcelona for his signature in July, but Mascherano insisted he "does not want to play for City".
"You can buy players, but you cannot buy history. Liverpool play with the history of the club. We do not have their money, but we are proud to play for Liverpool," he added.