The former Rajasthan chief minister was asked to step down from her post ten days ago in the wake of the BJP's debacle in the Lok Sabha elections in the state.
State BJP chief Om Mathur has already been relieved of his post, while two legislators backing Raje have been suspended.
The BJP's tally of 21 seats out of the total 25 in the state came down to four in the April-May Lok Sabha elections, while it lost power in the assembly elections late last year, paving the way for the Congress's return.
"She (Raje) has been asked to resign by August 28 and not to chair a meeting of the party's legislators Wednesday when a session of the state assembly begins," a party source said.
"She wants a respectable exit. She has made three conditions to resign -- that she be given a plum organisational post, the suspension of the two MLAs should be revoked and the new leader of opposition be of her choice."
But, sources said, Rajnath Singh asked her to first resign before her demands were considered.
Vasundhara Raje had refused to step down, stating that she alone could not be held responsible for the party's poll debacle in the state.
In a show of strength a few days ago, Raje drafted over 50 legislators to visit New Delhi to meet Advani and Rajnath Singh. However, Advani refused to meet them.