The CWC is the party's top decision-making body, is authrized to start the process of electing Gandhi's successor.
A Congress General Secretary, who wished not to be named, said: "Technically, Rahul Gandhi will continue as the party chief as his resignation has not been accepted by the CWC."
He said to elect a new President, the CWC needs to accept Gandhi's resignation first.
Party General Secretary, Organisation, K.C. Venugopal said the decision to call a CWC meeting will be a "collective" one.
Venugopal, who was in Kerala, told over phone: "A decision on calling a CWC meeting will be taken collectively."
Gandhi on Wednesday announced that he has resigned as the Congress President, taking blame for the party's rout in the Lok Sabha elections where it could win only 52 of the 542 seats.
In an open letter posted on his Twitter account which no longer described him as the Congress President, Gandhi, son of UPA Chairperson Sonia Gandhi, said the BJP's sweeping election win proved that the RSS aim of capturing the country's institutional structure was now complete.
"As President of the Congress party, I am responsible for the loss of the 2019 election. Accountability is critical for the future growth of our party.
"It is for this reason that I have resigned as Congress President," he said.
Two days after the election results were announced on May 23, Gandhi had said he would resign as the Congress chief.
Gandhi was defeated in the family pocket borough, Amethi in Uttar Pradesh, but he won from Wayanad in Kerala.
( With inputs from IANS )