The issue was up for deliberation on Wednesday during the meeting between the party leaders and former Congress president Rahul Gandhi and Congress' Punjab in-charge Harish Rawat.
The Congress is currently preparing an estimation of the number of leaders who are likely to quit.
However, sources say that people close to Singh are unlikely to quit the party.
The Congress leaders are watching his moves ahead of the new party formation and sources say that all the Congress members have distanced themselves after he worked out a "patch up formula" with the BJP.
Congress' Punjab in-charge Harish Rawat said "his decision will not make any difference to Congress".
"The party's performance will depend on the work of the new chief minister (Charanjit Singh Channi), and he is doing well," Rawat added.
Talking about Amarinder Singh, the former Uttarakhand chief minister said "it seems that he has killed the secular Amarinder within him... and how can he forgive the BJP for keeping the farmers on Delhi borders since the last one year."
The Punjab unit has been asked to keep an eye on the movements of the rebels and to pacify them ahead of the elections and dissuade them from joining the former Chief Minister.
Punjab Deputy Chief Minister Sukhjinder Singh Randhawa said "we have no fear... if Amarinder goes with the BJP, there must be some pressure on him."
Amarinder Singh on Tuesday said that he would soon announce the launch of his own political party to serve the interests of the people, including the farmers who have been fighting for their rights for almost a year now.
He said that he is hopeful of a seat-sharing arrangement with the BJP for next year's Assembly elections in the state, if the farmers' issues are resolved in their interest.
In a series of tweets, his media advisor Raveen Thukral quoted Amarinder Singh as saying: "The battle for Punjab's future is on. Will soon announce the launch of my own political party to serve the interests of Punjab and its people, including our farmers who've been fighting for their survival for over a year."