Mr Musharraf, who returned to Pakistan from self-imposed exile earlier this year, is currently under house arrest.
He is fighting a series of charges relating to his time in power, which began with him ousting Nawaz Sharif in a 1999 military coup.
His spokesperson described the proposed move as “reckless and ill-conceived.”
Mr Sharif told parliament: “Musharraf violated the constitution twice. He overthrew an elected government in 1999 and put everything into jeopardy. He sacked judges and imprisoned them.”
“He will have to answer for his guilt before the court,” he added.
Pakistan’s attorney general echoed Mr Sharif’s words in the Supreme Court, saying that the government intends to bring a treason charge against the former dictator for his imposition of emergency rule in 2007 which was followed by senior judges being placed under house arrest.
The court had already been hearing petitions from lawyers demanding that the former military ruler be tried for treason for those actions, but only the state can bring a high treason charge in Pakistan.
Mr Musharraf’s office released a statement saying that the former president had served his country with “selfless devotion and perseverance”.
“The Nawaz Sharif government is demonstrating recklessness in its intention to pursue unwarranted treason charges against former President Musharraf,” it added.
The former military ruler arrived in Pakistan earlier this year in high spirits saying he wanted to lead his party into May’s elections.
But he was disqualified from standing and ultimately placed under house arrest at his villa in Islamabad. He is accused of:
- Failing to provide enough security for murdered former Prime Minister Benazir Bhutto in 2007 when she returned to Pakistan to stand for election
- Detaining senior judges in 2007
He has been granted bail in both of these cases. However, he remains under house arrest because he was refused bail in connection with a charge relating to the assassination of the Baloch tribal leader, Nawab Akbar Bugti, who was killed in a military operation in 2006.
Mr Musharraf has described all the cases brought against him as politically motivated.
After his 1999 coup, Mr Musharraf ruled Pakistan for nine years before being defeated in elections. He left the country to live in self-imposed exile in Dubai and London.
Mr Sharif returned to power last month, winning elections by a landslide.