He was jailed after being ousted in a 1999 military coup led by Pervez Musharraf, Pakistan's current president.
Sharif is set to ignore the Saudi request and reaffirmed his intention to return home at a news conference in London.
On Friday, a court in the eastern city of Lahore issued an arrest warrant on Friday for Shahbaz in connection with a murder case.
Sohail Rahman, Al Jazeera's correspondent in Islamabad, said indications are Sharif would take a Middle Eastern carrier and arrive in Pakistan on Monday through Muscat.
Sharif has to take the detour since he remains banned from using Pakistani state airlines.
Sharif demanded Musharraf stop trying to block his way, asking: "Why is Musharraf so afraid that he is putting the country's solidarity at stake by involving the brotherly country of Saudi Arabia?"
He said it was Musharraf, and not he, who had broken his word.
Sharif said: "Today he is accusing me of breaching the contract when in fact he is the one who broke the constitutional pledge that he took when he was appointed army chief.
"Musharraf is shouting slogans of war against terror in order to win US support"
Ali Abu Hamza, Chichawatni, Pakistan
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"I am a Pakistani and it is my mission to go to Pakistan and save my country from the current turmoil and chaos."
Saad al-Hariri, son of assassinated ex-Lebanese prime minister Rafiq al-Hariri, has also called on Sharif not to return.
Sharif acknowledged that al-Hariri, who visited him in a Pakistani jail after his conviction in 2000 on terrorism and hijacking charges, had secured his release with an understanding that he would not return for a decade.
But Sharif said that al-Hariri later told him the period of exile was only five years, though he acknowledged that this was not mentioned in the document he signed.
Pakistani authorities have, meanwhile, detained more than 2,000 supporters of Sharif, his party said on Sunday.
"The way the government has acted has proven our point that there is no democracy under Musharraf, there is dictatorship in the country," Ahsan Iqbal, Sharif's spokesman, said.
He said authorities had detained more than 2,000 activists from Sharif's party in Punjab province, Sharif's political power base.
|Police have arrested hundreds of Sharif's |
supporters in advance of his return [AFP]
"Politically, they are very sacred of a big show of popularity upon his arrival," Iqbal said.
A provincial police official said 250 "trouble makers" had been picked up.
Ali Dayan Hasan of Human Rights Watch told Al Jazeera that many are being held on terror-related charges and some without charge.
He said the government plans to seal off Islamabad's airport to prevent people from reaching there to receive Sharif.
Media reports say a "VIP cell" at a 16th-century fortress is being prepared for Sharif.
Musharraf is facing political unrest as both Sharif and Benazir Bhutto, another former premier, are poised to return.
Bhutto will announce when she will go back to Pakistan on September 14, but has said it will be within "weeks, not months".
Musharraf has denounced both Sharif and Bhutto as corrupt and incompetent and blamed them for Pakistan's near-bankruptcy in the 1990s.