The 18-year-old centre-back was the subject of Roberto Mancini's attention on Sunday, as the Manchester City boss travelled to Italy to watch the Brazilian in action during Roma's 3-1 defeat to Sampdoria.
The report claims Mancini is prepared to let Joleon Lescott leave the Etihad Stadium at the end of the season, and he's identified the the 18-year-old as a possible long-term replacement.
The Brazil under-17 international joined Roma, initially on loan, from Corinthians, and he's impressed in the Italian capital.
But his composed performances have led to speculation Barcelona could be tempted to lure him to Spain - the Nou Camp club have a number of Brazilian defenders already on their books, including Dani Alves and Adriano.
And Marquinhos, speaking to Italian football site CalcioMercato, admitted he's flattered by the interest reportedly shown in him by the La Liga leaders.
Marquinhos said: "I like the interest of Barca yes, but now I have to think about it. I'm focused on Roma and complete the best season with this shirt.
"Now is not the time to think if one day I'll finish playing there."
Reports in Spain have suggested the Brazilian could be available for a fee in the region of £8m.
And Spanish newspaper El Mundo Deportivo claims Marquinhos's representatives believe Barcelona would be the perfect fit for their player.
Giovanni Cavallo, Marquinhos's agent, said: "Marquinhos meets all the requirements to play in a team like Barca. He's a young player, quality and has a strong personality."
The Brazilian youngster has made 16 starting appearances for the Rome-based club this term, despite his tender years.