"My lips are sealed. I cannot talk to you about it. This is between me and the President and I will talk to the President about it," Jung told reporters on the sidelines of a function here.
The LG was replying to a question on the possibility of formation of a new government in the national capital.
Asked whether the AAP has requested him to recommend fresh election in Delhi, Jung said no such proposal has come from the party yet.
On Tuesday, AAP leader Arvind Kejriwal had asked Jung not to dissolve the Delhi Assembly anytime soon, saying it will hold public meetings across the city to know whether the party should form the government again.
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However, AAP yesterday gave up efforts to form a government in the city with Kejriwal admitting that chances of returning to power were "negligible" in the current situation and apologised for quitting as Delhi Chief Minister.
Asked about protests staged by AAP members outside Tihar Jail where Kejriwal has been lodged after his arrest, the LG said no one should take law in their hands.
On the possibility of bringing Delhi Police under the Delhi government, Jung said, "Till Delhi remains a Union Territory, Delhi Police will remain under Home Ministry. I have no stand on this".
Meanwhile, Delhi Police Commissioner B S Bassi said 59 people, including AAP leaders Manish Sisodia and Yogendra Yadav, were arrested for violating prohibitory order outside Tihar Jail yesterday.
"We have arrested 59 people including Manish Sisodia and Yogendra Yadav. We will take action if someone breaks the law. There is Section 144 outside Tihar and we have been acting with maximum restraint since yesterday," he said.