The club have just lost star striker Lucas Viatri to injury and want Manchester City outcast Tevez to replace him.
In all likelihood, Boca will try to take Tevez on loan in January, something that would have huge appeal to the striker, who played his formative football there between 2001 and 2004.
Outcast: Carlos Tevez continues to train on his own at Manchester City's training ground
The Buenos Aires club's vice-president Jose Beraldi said: 'We'll make an attempt to get Carlos Tevez. I know it will be difficult but we will try.'
There is still a lot of affection for Tevez at Boca. When he visited their Bombonera stadium in May he was presented with an award for his services as a player.
Boca are not thought to have the money to buy Tevez, even though City are resigned to selling the 27-year-old for a cut-price ?20million when the transfer window opens in January.
However, City may yet be open to loan deals if they find themselves short of offers to buy him.
Tevez's representatives are still hopeful that increasing interest from the big Italian clubs will firm up in January and there is also the possibility that Brazilian club Corinthians will return to the table after their attempt to strike a deal collapsed in August.
Homecoming: Tevez is wanted at his old club in Buenos Aires, where he is still idolised
It is understood that Tevez's aide Kia Joorabchian was with Corinthians' director of football Edu the former Arsenal midfielder at the weekend and the topic of another move for the former City skipper was again raised.
Tevez is waiting to appear before a City disciplinary hearing for allegedly refusing to come on as a substitute at Bayern Munich three weeks ago.
Meanwhile, his team-mates face Villarreal in a make-or-break Champions League tie tonight with manager Roberto Mancini reluctant to discuss the Tevez situation.
Homesick: The striker used his two-week suspension to return home
Having taken only a point from their first two games in Europe, City need to beat the Spanish club if they are get their hopes of qualifying for the knockout stages back on track.
'Villarreal are a good team. They are used to playing Champions League, they have done so many times in the past 10 years,' said Mancini. 'But for us I don't think it is as important to play well or not well it is important we win this game. I think if we win this game I think we can win also the group.'
Mancini has given the club a pre-match boost by revealing he wants to stay at City for the foreseeable future.
'I would like to stay here for many years,' he said. 'My feeling here is good. I started here two years ago. I have worked hard to build a good team and I would like to stay here for three or more years. At this moment Manchester City are considered one of the best clubs in the world.'
Mancini, who has 18 months left on his current contract, is highly regarded at home in Italy and is one day tipped to manage their national team. But he added: 'A new contract is not important right now. In football, things can change if you lose a few games. But I am not thinking about going back home.'
City will welcome Tevez's compatriot Sergio Aguero back to the team after he recovered from a groin injury. However, it is David Silva who is winning rave reviews after some excellent performances for both City and Spain.
Silva lining: Roberto Mancini believes David Silva is one of the form players on the planet
Mancini said: 'I think at the moment Silva is one of the best players in Europe and the world. I think Silva can play for Real Madrid, Barcelona. He is an incredible player.
'He has improved a lot in the last year as a guy and as a player. I saw him for the first time when I played in the Champions League several years ago Inter versus Valencia. He was young then but he was incredible.'
City face neighbours Manchester United in a huge game at Old Trafford on Sunday. Last night it emerged that Mark Clattenburg will referee the game.
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