According to the sources, a way forward is likely only after Rahul is back from his foreign visit.
The Congress vice president is expected to return towards the weekend or early next week.
"Talks were held to diffuse the situation. But a call in this connection will be taken only after Rahulji is back from abroad," a source said.
The four-time chief minister of the hill state had also earlier conveyed to the party's central leadership that he would not contest the upcoming assembly polls if "current situation" persisted.
While Singh is firm on his demand, the sources said that a section in the AICC feels that any disruption in the party unit in Himachal Pradesh, one of only six states being ruled by the party, "just ahead of the polls" will not augur well in view of the party's prospects.
Karnataka, Mizoram, Punjab, Puducherry and Meghalaya are the other states where the Congress is in power.
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