The 25-year-old Paraguayan enjoyed a successful debut season in the Bundesliga last term, scoring an impressive 19 goals in 33 league games for Dortmund following his move from Chilean team Colo Colo.
His efforts were good enough to earn him third-place in the race for the Bundesliga equivalent of the Golden Boot and also served to attract interest from the likes of Napoli, Fiorentina and AC Milan.
But Barrios remained coy on his future when quizzed by Spanish newspaper Ole.
"I still have four-years on my contract.," he said.
"However, they say that Milan, Fiorentina, Manchester City and Napoli would like to buy me."
Barrios was embroiled in a controversial tug-of-war ahead of the World Cup as both his country of birth – Argentina – and Paraguay fought for his services.
But the Buenos Aires-born front-man chose Paraguay ahead of Argentina before the World Cup and went on to produce five solid performances as the Paraguayan’s reached the quarter-finals.
Should Roberto Mancini follow up his interest in Barrios it could see him linking up with fellow Paraguayan striker Roque Santa Cruz in the City front-line at Eastlands.
The Blues, meanwhile, took a step closer to securing the services of England midfielder James Milner on Thursday, with Aston Villa manager Martin O’Neill revealing that Milner can go, providing City match Villa’s value of the player.
By James Martini
