City have been short up front during December due to injuries to all three of their senior strikers; Sergio Aguero, Edin Dzeko and Stevan Jovetic.
That has led to speculation the club - who allowed another striker, Alvaro Negredo, to join Valencia in August - could seek reinforcements in the forwards department, with Bony a possible target.
But any move for the Ivory Coast international, who has scored eight goals this season, would be complicated by the fact City currently have no more room to register non-homegrown players in their squad.
Further changes to the squad would therefore be necessary and - with additional European Financial Fair Play restrictions in place - Pellegrini has indicated there is unlikely to be much movement.
The Chilean said: "I think that is just one of the 20 or 30 names I have read from the beginning of the season until today that we are (supposedly) interested in.
"I don't think we are going to be too busy in this window
We have restrictions about the amount of money and about the number of players we can put in the Champions League, so I don't think it will be a special transfer window for our team.
"We have the option to do it - we will see in the whole month of January what we are going to do about that - but it is not a major concern."
Bony would also not be available immediately because, like international team-mate Yaya Toure, he is due to play in the African Nations Cup.
City are expecting to lose the services of midfielder Toure after their FA Cup third round tie with Sheffield Wednesday on January 4.
Pellegrini said: "Yaya must go on January 5
He can play this week - tomorrow and on Sunday."
Toure is available again to face Sunderland on New Year's Day after missing Sunday's draw against Burnley.
Captain Vincent Kompany, however, remains on the sidelines after hamstring and calf problems and is unlikely to face Sunderland or Sheffield Wednesday.
The champions will also be without strikers Aguero and Dzeko until later in January.
Sebastian Larsson could yet make Sunderland's trip as he prepares to play through the pain barrier.
The Sweden international limped off with an ankle problem 57 minutes into Sunday's 0-0 Barclays Premier League draw at Aston Villa, but was expected to train on Wednesday to give himself a chance of retaining his place in Gus Poyet's team.
Fellow midfielder Liam Bridcutt was not so fortunate and will miss out after suffering concussion at the weekend, while full-backs Patrick van Aanholt (shoulder) and Anthony Reveillere (calf) are due to resume training on Monday.
Sunderland head coach Poyet is expecting Emanuele Giaccherini and Ricky Alvarez to come to the fore during the second half of the season.
The Black Cats will head into 2015 having reached the halfway stage of the Barclays Premier League campaign sitting in 14th place in the table, but just four points above the drop zone and with the man at the helm desperately hoping for an injection of firepower during the January transfer window.
However, with Italy international Giaccherini now back in harness having shaken off an ankle injury and Argentina counterpart Alvarez - on loan for the season from Inter Milan - having resumed following a knee problem, Poyet is hoping the invention they can provide will help to giving him a new cutting edge.
Asked what they could bring, the Uruguayan said: "In terms of their position on the pitch, it's massive
It's their value, their ability, why they played, Giaccherini at Juventus or Ricky Alvarez at Inter Milan
They played for top, top teams in Italy and you would expect them to really make a difference.
"He is different, Giacchy, to Ricky, because Giacchy had a very difficult [first] year in England in a team struggling all season, so he learned everything
And, like I have said here many times before, he came back in pre-season at another level - he was like a new signing.
"Ricky is still adapting to this incredible league in which nobody gives up and every ball, every minute, every second is important, so it's totally different.
"I know the players know that, but until they are on the pitch, up and down and stop and break and break and break and break, then you start realising and adapting to what you need, so slowly.
"I am not in a hurry with Ricky
We are going to use him at the right time in the right games at the right moments, but like any other foreign player, it's going to take him a while."
Source : PA
Source: PA