Off contract in June, Garcia was willing to return to former club Barca this month, but that has been ruled out by the club's presidential candidates. Instead, Barca aim to take Garcia at the end of the season as a free agent.
However, Mundo Deportivo says PSG are now jumping into the battle.
Those close to Garcia's camp say contact with PSG has been received, though he remains hopeful of securing an agreement with Barca.
But PSG are willing to meet City's asking price of €5m up front plus €5m in bonuses to sign the defender immediately. Barca's football had agreed these terms with City for Garcia before the intervention of the candidates.