MK Amichai Chikli (Yamina) is working to advance a deal with the coalition in exchange for his support of the state budget.
The proposed deal would see Chikli become a one-man party, allowing him to join any party he wishes to join ahead of the next elections, Yediot Aharonot reported.
The Yamina party could declare Chikli to be someone who left the party, and place harsh sanctions on him, blocking him from running in any of the existing parties in the next elections.
However, though the Yamina party is not rushing to agree to Chikli's request, it is possible that there will be no choice but to approve it, since the coalition's success depends on his support.
Earlier this week, the coalition reached an agreement on a state budget, approving the bill and sending it to the full Knesset for its support.
However, it is not clear that the budget will pass in the Knesset plenum, leading Finance Minister Avigdor Liberman (Yisrael Beytenu) to turn to the Joint Arab List for support.
In an interview this week with Channel 12 News, Liberman said: "I am not negotiating with the Joint Arab List - we have our own government. If we have to, we will get one or two of them to support it without a moment's hesitation. We have a government majority and all it takes now is 61 Knesset MKs."