After being nominated to his old job by Boris Yeltsin in a shock weekend government shake-up, Mr Chernomyrdin met parliamentary leaders yesterday to discuss a deal.
The Communist speaker of the lower house, Gennady Seleznyov, said an agreement had been reached with the acting premier on "the principles of a coalition government", which would be accompanied by a document requesting Boris Yeltsin not to interfere with its workings.
A "pink" coalition government in Russia would be yet another reversal for the weakened Mr Yeltsin, as it would be tantamount to pulling back from his much-vaunted commitment to the reform process.
The president made what amounted to a humiliating appearance on national television yesterday to explain his decision to reappoint Mr Chernomyrdin only five months after firing him, and to dismiss the short-lived government of 36-year-old Sergei Kiriyenko amid an economic crisis.
A coalition government would also be certain to alarm western investors, who were yesterday awaiting delayed details of Russia's plans to reschedule $20bn of short-term debt. Nor would it please the International Monetary Fund, which has been pressing for radical economic measures in Russia in return for western support.
Despite this, Mr Chernomyrdin may make some concessions, including handing the Russian Communists some ministries, if it means political co-operation, and mollifying a deeply disenchanted public.
The largest opposition party, the Communists, have had occasional ministers in power before, but pleas for a cross-party "government of national unity" have been ignored.
Yesterday, as the bargaining process swung into motion, they maintained their public attack on the Kremlin. Its leader, Gennady Zyuganov, said the Communists intend to continue impeachment proceedings against the President and condemned the"complete moral and political bankruptcy of the present anti-people regime."
The faction would only confirm Mr Chernomyrdin in post if he agreed to fundamental policy changes, he said.
During his TV address, Mr Yeltsin appealed to Russians to support his new premier, praising Mr Chernomyrdin's "weight and experience". He made clear that he saw the 60-year-old former energy boss as his successor after the next elections in 2000.
President Yeltsin's sudden sacking of the government - which follows hot-foot on last week's rouble devaluation debt default - saw the departure of a leader regarded in the West as one of the country's most promising young reformers.
Complaining of "rampant monopolies", Boris Nemtsov, 38, a deputy prime minister under Mr Kiriyenko, announced that he did not wish to take part in Mr Chernomyrdin's cabinet.