However, a leader in the know said that if no party does so within the next eight-ten days, the chances of the assembly being dissolved would be very high.
Also, if the governor recommends the imposition of President's rule and the Union cabinet approves it, the UPA government would face the onerous task of getting parliamentary sanction for the move.
Getting the approval of both houses of Parliament for extension of President's rule in a state within six months is a constitutional requirement.
The BJP-led Arjun Munda government fell after the JMM withdrew support to it on January 8, about 28 months after it was formed on September 11, 2010.
So far, the Congress and JMM have not been able to sort out their differences over government formation - with both parties staking claim to the chief minister's post.
A powerful section of the Congress is not in favour of imposing President's rule in Jharkhand and is, at the same time, unwilling to let JMM lead the coalition.
JMM leader Hemant Soren met the governor in Ranchi on Saturday, seeking more time on the ground that he was in a dialogue with like-minded parties over the issue.