The 43-year-old received widespread acclaim for his portrayal of ganglord Sardar Khan in Anurag Kashyap's Gangs of Wasseypur and believes the film, which was part of the official selection at the 65th Cannes International Film Festival, gave him greater exposure.
Speaking to PTI, Bajpayee said: "I think somewhere Anurag Kashyap is my ticket to international films. I keep pestering him to get me scripts. I have got offers and that came through Anurag.
"I have received offers... I am going through a script. It has come from an American independent filmmaker and not from any studio. I would love to do an international film."
Several Bollywood stars have made the transition to Hollywood, including Anil Kapoor, Anupam Kher and most recently Irrfan Khan and Tabu, who had key roles in Life of Pi.
"I remember telling Tabu that if I get to shoot one scene in Oscar-winning director Ang Lee's film I will do it. As I believe life is short, I don't know when I will get the next chance," Bajpayee said.
The actor, who said that it was his dream to play Devdas, explained that he accepted a role in Veer Zaara just to work with Yash Chopra.
"I did Veer Zaara for Yash Chopra. I did the film thinking, 'When will I get the opportunity to get directed by Yash Chopra?'... so I did it purely for him.
"It was just to get an experience of working with him. But at the same time one should feel the urge to do the film."
Bajpayee stars in Neeraj Pandey's Special Chabbis with Akshay Kumar, releasing on February 8.
Watch the trailer below: