According to what has been shown so far, the US and Iran have leaned towards choosing Pakistan rather than Oman as a mediator for diplomatic negotiations. Oman has played this role in negotiations between the US and Iran on Iran's nuclear program. But that was in pre-war times.
The opportunity for Pakistan to hold the flag to fly is there. Pakistan is a neighbor to Iran. The relationship between Pakistan and Iran is not entirely smooth, but Pakistan is still the least hostile neighbor to Iran and there is no US military base on Pakistani territory. Economic and trade relations between Iran and Pakistan are also not bad. The two sides have a common enemy in the Belushistan region.
Also because it is a neighboring country of Iran, Pakistan has a practical interest and urgent need to quickly end the war between the US and Israel with Iran. Moreover, despite establishing military, defense and security cooperation relations with a number of Arab dynasties in the Gulf region containing US military bases, Pakistan shows a neutral attitude in the war that the US and Israel launched against Iran, and even opposes this war.
Government leaders and military officials in Pakistan, who have established a friendly and trustworthy relationship with US President Donald Trump, have given Mr. Trump the opportunity to build his reputation in dealing with the recent military conflict between Pakistan and India. Enhancing Pakistan also helps Mr. Trump have more trump cards in dealing with US relations with India and China. Mr. Trump does not forget that he has been nominated by Pakistan for the Nobel Peace Prize.
Pakistan has the opportunity to play the role of intermediary diplomacy, but successfully fulfilling this role is a different and much more difficult and complex matter.