Chief Justice LHC is the father-in-law of Ali Afzal Sahi, Khan told anchorperson Asma Shirazi, on Tuesday.
According to PM's adviser, the CJ approached him, and asked for his role for Sahi's success in the polls.
He went on to add that he has all the evidence of the meeting, adding another judge of the high court and two officials were a witness to the meeting.
The development comes at a time when a judge of the Supreme Court is facing the charges of alleged misconduct.
A week ago, the Public Accounts Committee (PAC) gave the authorities concerned a directive to provide information about the assets of Supreme Court judge Sayyed Mazahar Ali Akbar Naqvi.
13 out of 14 members of the PAC voted in favor of calling for the specifics of the judge's holdings during a meeting that was presided over by Noor Alam Khan.
The sole senator who disagreed with the decision was Senator Mohsin Aziz, a PTI member.
The chairman of the committee requested that the Pakistani Auditor General look into the various types of land that the judge owns and provide him with a report. He also asked the authorities concerned to submit his travel records.
Khan further instructed the National Database and Registration Authority to give him a list of the judge's family members.
A week prior to PAC's directives, National Assembly requested the committee conduct a special audit of judge's accounts and sources of income in response to the charges of corruption against him. It came amid an ongoing dispute between the parliament and the judiciary.
Numerous references have been filed before the Supreme Judicial Council (SJC) against Justice Naqvi for alleged wrongdoing and possessing assets beyond their known means of income.