Amarinder made the remark after he called on Rahul Gandhi at the Congress Vice President's residence in New Delhi to congratulate him on the Congress victory in the February 4 Punjab assembly polls, where it bagged 77 of the 117 seats.
"Now is the right time to elevate Rahul Gandhi as party President. I have been maintaining this for the past one year," Singh said.
After a 10-minute meeting with Gandhi, the Punjab Congress President and Congress Legislature Party leader told the media: "It was a courtesy call. There was no discussion on Cabinet formation during the meeting."
Singh invited Rahul to attend the swearing-in ceremony slated for Thursday morning in Chandigarh.
This was the first meeting between the two after the Punjab elections.
Rahul expressed the confidence that Punjab will once again rise to its true potential under a Congress government.
Amarinder also lashed out at the Aam Aadmi Party (AAP) for refusing to accept its defeat gracefully.
"Instead of acknowledging that his party failed to connect with the voters of Punjab, (Delhi Chief Minister) Arvind Kejriwal is making allegations about (tampering of) Electronic Voting Machines. Incidentally, his own party workers were guarding the EVMs," said Singh.
"AAP workers were camping outside centres where the EVMs were stored. It is evident that Kejriwal is unable to digest loss of election as well as face after the assembly poll outcome, which he was hoping to leverage to further his national ambitions," he added.