The Congress sees such an alliance, or "maha gathjod" to put up a credible fight against the BJP in the assembly elections, expected in November.
Over the past weeks, a spate of political defections, primarily from the JVM-P, to the saffron party has rendered other political formations vulnerable.
According to JMM insiders, the Shibu Soren-led party may agree on a seat-sharing pact with the Congress if it is allowed to contest at least 43 of the 81 seats but is unwilling to align with JVM-P.
Speculations over the alliance grew stronger after former Congress MP Furkan Ansari met JVM-P chief Babulal Marandi last week.
Congress state president Sukhdeo Bhagat, however, has sought to play down the significance of the meeting.
He said the Congress was already in a coalition with the JMM and the Lalu Prasad-led Rashtriya Janata Dal and that they may go in for an alliance, adding that the party had so far not approached any regional forces for a pre-poll alliance.
The Congress wants the JVM-P and the AJSU in the wider alliance, but the JMM — a major stakeholder in Jharkhand — is unhappy with such a suggestion.
The JMM was the only party that won two seats from the state in the Lok Sabha polls. The remaining 12 seats were bagged by BJP candidates. Political observers say the fact that five legislators from the JVM-P and JMM's Simon Marandi had joined the BJP over the past three weeks should force the two parties to consider a common stand against the saffron party.