The police had filed the application before the sessions judge G A Sanap on October 8.
The court this week framed charges against Sayed Zabiuddin Ansari alias Abu Jundal, one of the key conspirators of the Mumbai terror attack.
The prosecution today told the sessions court that Headley had not been tried under Indian law for 26/11 conspiracy.
"An American court is not competent to try offences under Indian Penal Code. The charges for which Headley has been convicted by the US court and the charges we are pursuing against him are entirely different," said Special Public Prosecutor Ujjwal Nikam.
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The judge also sought to know why the Mumbai police did not launch an investigation after the US took Headley's custody.
Earlier, the Mumbai police had moved an application before the sessions court seeking issuance of Letter of Request (LR) against Headley for his production through video conference in connection with the 26/11 case.
The present application says that Headley deserves to be tried by the Mumbai court along with Jundal as both are conspirators and abettors.