Naeem Panjutha said the Islamabad High Court will hear the appeal on Wednesday.
Khan, 70, was arrested and taken to prison on Saturday after being convicted of failing to properly declare gifts he received while in office. He was sentenced to three years in jail.
In the appeal, Khan’s lawyers said the former premier’s conviction should be set aside and declared “illegal and without lawful authority”. It also requested the court acquit Khan, claiming he was arrested illegally.
Mr Panjutha told reporters outside the high court on Tuesday that Khan's legal team were also seeking better facilities for him through another petition filed in the court.
Khan's lawyers visited him in prison on Monday and were preparing to file a bail application after receiving power of attorney, his spokesman Raoof Hasan told AFP.
Mr Hasan said Khan was being held in a so-called "C-class cell" at the century-old prison in Attock, near the capital Islamabad.
The cell has a mattress on the floor and only enough room for a prayer mat, he said. There is little access to daylight and while there is a fan, there is no air-conditioning unit.
"He is being held in deplorable conditions not fit for any human, but he is in good spirits," Mr Hasan said.
"He said to 'tell the people that I will not compromise on my principles'."
Mr Panjutha said the former prime minister's legal team had already petitioned a court seeking better prison facilities for him.
Khan's jail term has ruled him out from contesting the general election due later this year after the current parliament's term ends. Pakistani law prohibits anyone with a criminal conviction from holding or running for public office.
He told The National last month that he was facing more than 180 cases filed since after he was ousted from office by a vote of no confidence in April last year.
His Pakistan Tehreek-e-Insaf party and critics have said the former premier was being politically victimised by the government of current Prime Minister Shehbaz Sharif, a charge the government denies.
Mr Sharif, who replaced Khan after his ouster, said on Tuesday that he would step down on Wednesday and hand over charge to a caretaker government that would run the country until elections were held.
Khan was arrested and held for three days in May in connection with the same case in which he was convicted on Saturday. His detention sparked deadly violence, with his supporters taking to the streets in the tens of thousands and clashing with police.
It also prompted the crackdown that saw almost all of the top leadership of his Pakistan Tehreek-e-Insaf (PTI) party arrested or forced into hiding, leaving the party scrambling to set up a replacement decision-making body.
The reaction to Khan's jailing so far has been vastly different to the outpouring of rage that followed his first arrest, even on social media, with half as many Facebook posts mentioning Khan's name.
"The muted response to his arrest is because of the full-throttle crackdown on PTI workers after the first arrest," columnist Usama Khilji told AFP.
"The arrests of PTI workers post the May arrest of Imran Khan coupled with draconian laws passed in haste by [the coalition government] have had a chilling effect on Pakistani citizens."