The payments processor has traditionally dealt in credit and debit cards but has moved into mobile payments as contactless systems like Apple Pay, which simply let users tap their device to a receiver, become more popular.
Kelly said the company is thinking ahead to an eventual move beyond physical payment methods and traditional points of sale.
"Over time we want to talk much more about payment credentials, which could be real — a real form factor — or they could simply be numbers in the digital world," Kelly said. "The word[s] 'merchant locations' or 'businesses' are also going to become obsolete."
A growing catalog of connected devices — cars, refrigerators and washing machines all connected to a global internet — means broader purchasing power, he said.
"We at Visa are trying to make sure that we work with manufacturers around the world to create an on-ramp to facilitate payments from any of those locations," Kelly said. "We just want to be in the middle of that."
Kelly does draw a line for new-age payment methods, though. He told CNBC Visa wouldn't process transactions in bitcoin.
Kelly also discussed his leadership style, years in the White House and decision to expand Visa's 401(k) program.