The Saudi monarch asked Sharif to take a clear position on Qatar during their meeting in Jeddah on Monday, The Express Tribune reported, citing diplomatic sources.
"Pakistan has told Saudi Arabia it will not take sides in the brewing diplomatic crisis in the Middle East after Riyadh asked Islamabad 'are you with us or with Qatar'," the paper said.
Pakistan has been treading a careful path since Saudi and other Gulf countries snapped diplomatic ties with Qatar after accusing the oil-rich country of supporting terrorist groups. But Saudi wants Pakistan to side with the kingdom, it said.
Citing a senior government official, who was briefed on the talks at the monarch's palace in Jeddah, the paper said that Pakistan would not take sides in any event that would create divisions within the Muslim world.
"Nevertheless, in order to placate Saudi Arabia, Pakistan offered to use its influence over Qatar to defuse the situation. For this purpose, the prime minister will undertake visits to Kuwait, Qatar and Turkey," it said.
Sharif, accompanied by army chief General Qamar Javed Bajwa and other senior officials, travelled to Jeddah on Monday to discuss the emerging situation in the Gulf world.
Prime Minister Sharif's mediation visit to Saudi did not achieve any immediate breakthrough.
According to an official statement, Sharif met King Salman in Jeddah and urged an early resolution of the impasse in Gulf in the best interest of all Muslims.
Saudi Press Agency (SPA) said King Salman and Sharif discussed the "latest regional developments" in addition to bilateral relations.
Salman told Sharif that "the fight against extremism and terrorism is in the interest of all Muslims and the Ummah".
The SPA, while announcing the severing of relations with Qatar, had said it had been done for "protection of national security from the dangers of terrorism and extremism".
Qatar, meanwhile, has indicated that it was willing to address concerns of the countries that ended diplomatic relations with it.
The current crisis in the Gulf is said to be the gravest that the Gulf Cooperation Council has faced in its nearly four decades of existence, although Qatar's relations with Saudi and some other Arab neighbours have not always been good.
Other diplomatic efforts have so far not been successful in defusing tensions either.
Kuwait's Emir Sheikh Sabah al Ahmad, who has been leading the diplomatic initiative, vowed to continue his efforts to resolve the ongoing crisis despite remaining unsuccessful in his earlier bid.
Saudi, UAE, Bahrain and Egypt had cut off diplomatic ties and transport links with Qatar on June 5 on the pretext that its policies are fuelling extremism and terrorism.
The crisis erupted late last month over fears that Qatar was trying to improve its ties with Iran, which Saudi Arabia and its allies wanted to be isolated.