There is a strong though unconfirmed buzz that the 52-year-old former cricketer and commentator is drifting towards Arvind Kejriwal's Aam Aadmi Party (AAP), which is campaigning aggressively in Punjab ahead of elections in the state next year.
Some reports suggest that Mr Sidhu, who is also a popular TV personality, could be AAP's chief ministerial candidate.
Mr Sidhu was nominated to the Rajya Sabha in April. He was upset with the BJP when he was asked to give up his Amritsar constituency for Arun Jaitley to contest from there during the 2014 national election.
On the first day of the Monsoon Session of Parliament, Gurdeep Singh Sappal, OSD to Vice-President Hamid Ansari tweeted:
Sidhu had represented the Amritsar constituency for 10 years.
Sidhu’s wife Navjot Kaur is a parliamentary secretary in the Punjab SAD-BJP govt, who may also resign, the newspaper added.
She had announced her resignation on Facebook earlier this year but later changed her mind.
AAP has been actively campaigning in Punjab for the upcoming assembly elections in 2017. Delhi chief minister and party chief in Punjab early Monday to offer his apology by performing voluntary service after the party's 'Youth Manifesto' carried a picture of the Golden Temple, along with the AAP election symbol: A broom.