He plans to first stop in New York and Secretary-General Antonio Guterres's spokesperson Stephane Dujarric said a meeting between them was likely.
"My understanding is that the meeting if it happens the meeting was requested by the Pakistan mission and the Secretary General is always happy to meet visiting foreign ministers," Dujarric said on Tuesday.
Guterres, who was in Portugal for the Lisbon Green Capital initiative and other meetings, is travelling back to New York and the visit will depend on him and Qureshi synchronising their schedules.
A neighbour of Iran, Pakistan is trying to insert itself Teheran-Washington confrontation and take on a mediating role.
Qureshi had met Iranian President Hassan Rouhani and Iranian Foreign Minister Javad Zarif in Tehran on Sunday and Faisal bin Farhan Al-Saud on Monday.
Pakistan Prime Minister Imran Khan had said in September after a meeting with US President Donald Trump that he had been asked to mediate to bring down the tension.
However, there was no confirmation of the request by the US.
Tensions between Washington and Teheran neared a flashpoint this month after Iranian Major General Qassim Soleimani, the commander of the Quds Force, was killed in a US missile strike in Iraq and Iran retaliated with rocket attacks on bases in Iraq where US troops are stationed.
However, both sides drew back from the brink and have indicated that there would be no further escalation for the time being.
(Arul Louis can be contacted at arul.l@.in and followed on Twitter @arulouis)
( With inputs from IANS )