According to sources, Singh met Sonia at her residence and is understood to have told her that Bajwa, his known detractor, has failed to take the party along with him leading to major dissidence against his leadership.
"I had met her to inquire about her health as she was unwell and was in hospital when I was abroad. It was a courtesy call," Singh told PTI.
He later said, "Bajwa cannot secure victory for the party".
Singh is understood to have told Sonia that if the Congress has any chance left in Punjab, the party has to change Bajwa, whom he alleges has failed to take the party with him and bring in fresh blood and vigour into the party.
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Sources that Singh has also met Congress Vice President Rahul Gandhi and raised the issue of leadership change with him.
The meeting has come at a time when the strains between the ruling Akali Dal and BJP are growing, with a section of the BJP in the state seeking severing of ties with SAD and going it alone in the next assembly elections.
Punjab goes to polls in January 2017. Congress has successively lost to the SAD-BJP combine in the previous two assembly polls.
Party sources also did not rule out the possibility of the 72-year-old leader being made Congress' Chief Ministerial candidate in Punjab where assembly elections are due in 2017.
A senior party leader, who declined to be identified, said the high command could designate another person as the party's Deputy leader in the Lok Sabha soon.
Seeking to dismiss speculation that Amarinder was set to join BJP, the leader said it showed the stature of the former Punjab Chief Minister as "no one can ignore him".