Burkhalter, 54, is publicly downplaying such talk but Swiss media are reporting that the popular politician is eying a run to succeed South Korean Ban Ki-moon, whose second five-year mandate runs out at the end of next year.
Several media outlets have said that Burkhalter and his department are working on a potential candidacy.
The speculation is fed by the success of the Neuchâtel native in his role as a mediator in the Ukraine crisis last year as president of the Organization for Security and Co-operation in Europe (OSCE).
The economist and member of the centre-right Liberal party also served as Swiss president in 2014 and was voted “Swiss of the year” last year.
“It’s never the office that excites me but the opportunity to do something,” Burkhlater told Schweizer Illustrierte magazine in an interview published on Monday.
“In today’s world, I find it important to get involved for peace and security, no matter in what capacity.”
Ban Ki-moon is not expected to seek a third mandate, giving rise to speculation about who may succeed him.
According to convention, his successor should come from Eastern Europe.
However, a candidate from another region could be considered if countries cannot agree on a representative from an Eastern European country, or if a country, such as Russia, should exercise its veto.
The other prospect bolstering Burkhalter’s chances are rumours, reported by Swiss media, of the nomination of Burkhalter and the OSCE for a Nobel peace prize.
“I think it is wrong to speak publicly about such a nomination because the work of the organization (OSCE) should not be personalized ,” Burkhalter told Schweizer Illustrierte.
“The OSCE as a whole is important,” he said, highlighting its role in ensuring dialogue in conflicts between the East and the West.
Burkhalter added that he wanted to write a book about his experience with the OSCE and the opportunity it offered to Switzerland during its presidency of the organization to take “more responsibility for peace in the world”.