The 28-year-old Peru international attracted attention from across Europe after scoring twice in the FIFA Club World Cup final earlier this month.
Atletico Madrid, Juventus and Fiorentina are also thought to be interested, but the former Bayern Munich striker told Globo Esporte that he wants to remain in Brazil.
He said: "I will stay. I have a contract and I am very happy playing for Corinthians."
Guerrero joined Corinthians in July for £3m from Hamburg and is under contract with the world champions until 2015.
The Brazilian side are keen to ward off interest in the forward and have reportedly placed a £30m asking price on him.
Guerrero was on target in the semi-final of the FIFA Club World Cup, against Egyptian side Al-Ahly, before scoring the winner in the final against Chelsea.
He previously spent ten years playing in Europe, all in Germany's Bundesliga, having joined Bayern Munich in 2002 and left for Hamburg in 2006.