The City striker has been on compassionate leave for a fortnight, since his wife Vanesa gave birth to their daughter six weeks prematurely.
Tevez looked set to clash with City manager Roberto Mancini when the Italian said he thought it was time for him to return to England, following Sunday's draw against Liverpool at Eastlands.
Tevez: training in Argentina
It is understood Tevez did not take kindly to those comments, but the situation could well be resolved, as he is hopeful he will hear his daughter has improved enough for him to leave South America.
This would mean he could return on Thursday and train ahead of Saturday's important Barclays Premier League match at Chelsea.
Kia Joorabchian, Tevez's adviser, said: 'When your child is in intensive care, it is a serious matter. Obviously, Carlos is having to go through a difficult period.
'He was determined to get back for the Liverpool game, but unfortunately the situation didn't get much better. However, his daughter has improved and Carlos wants to get back and play.'
Tevez will clearly not be back for City's FA Cup tie at Stoke on Wednesday. It is understood Joorabchian was angry when he heard about Mancini's comments on Sunday, but the City boss is not always helped in such situations by his limited English.
Tevez received a text from Mancini on Sunday asking about his daughter's health, but most communication has taken place between Joorabchian and City's football administrator Brian Marwood.
Joorabchian said: 'Carlos is training daily with Argentina's team and spending one-and-a-half to two hours there. He is a professional. He understands that side of it.'
City need Tevez back in action soon. He was their best player in December and January and they have struggled without him.
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