Real Madrid have sounded out the Bundesliga side about the Paraguay international, only to be told that City were showing strong interest in a player who has hit 13 goals in 23 games this season.
Liverpool and AC Milan have also been linked with the 26-year-old, who is nicknamed La Pantera - The Panther - for his predatory qualities in the box.
Top cat: Lucas Barrios, also known as the Panther, is wanted by Manchester City
City are interested in signing Bosnia and Herzegovina striker Edin Dzeko from Wolfsburg regardless of Tevez's future, but they also face competition for him from Madrid and Juventus.
Barrios is another handful, standing at 6ft 2in and looking built for the Barclays Premier League. He would also be relatively cheap, with the bidding expected to start at about £15million.
His goals have helped Dortmund stack up a surprise 11-point lead at the top of the Bundesliga, but the club are seen as vulnerable to bids for their top players.
Goalkeeper Roman Weidenfeller looks set to snub a new contract offer to join Aston Villa on a free at the end of the season and Serbia defender Neven Subotic - a target for Arsenal - could also leave.
It is less than 18 months since Dortmund paid £3.6m to take Barrios from Chilean side Colo Colo and he has hit an impressive 33 goals in 56 appearances.
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