A Western diplomat went as far as to say that it was now "highly probable" Iran and world powers would agree to such a move, and that the extension would be months not weeks.
"As it's highly improbable that we will finalise in Vienna before the weekend, it is highly probable that there will be a wish to continue to negotiate in the coming months," the diplomat said on condition of anonymity on Tuesday.
After a decade of rising tensions, the mooted accord between Iran and the five permanent members of the UN Security Council plus Germany is aimed at easing concerns that Iran might develop nuclear weapons and silencing talk of war.
Kerry said he would return to Washington to discuss with President Barack Obama "the prospects for a comprehensive agreement, as well as a path forward if we do not achieve one by the 20th of July, including the question of whether or not more time is warranted".
He told a news conference after two days of talks with Iranian counterpart Mohammad Javad Zarif that there had been "tangible progress on key issues, and we had extensive conversations in which we moved on certain things", although "very real gaps" persisted between the two sides.
Zarif, in a separate news conference, said that although he still hopes a deal would be possible by Sunday, he believed enough progress has been made to justify a continuation.
"As we stand now, we have made enough headway to be able to tell our political bosses that this is a process worth continuing," Zarif said. "This is my recommendation. I am sure Secretary Kerry will make the same recommendation."
An interim accord struck in November between Iran and the five permanent members of the UN Security Council plus Germany expires on July 20.
Extending the deadline has always been a possibility in order to keep the parties talking, but Washington in particular has stressed it will not agree to such a move without key concessions from Iran first.
Iran denies seeking the atomic bomb and wants the lifting of crippling UN and Western sanctions.
The six powers want Iran to dramatically reduce in scope its nuclear programme for a lengthy period of time and agree to more intrusive UN inspections.
This would greatly expand the time needed for the Islamic republic to develop a nuclear weapon, should it choose to do so, while giving the world ample warning of any such "breakout" push.
Iran on the other hand has stated it wants to expand its nuclear facilities, insisting they are for purely peaceful purposes and that it has the perfect right to nuclear activities under international treaties.
Both sides are also under intense pressure from hardliners at home - midterm US elections are due in November - and both are wary of giving too much away after several months of talks.
Key US lawmakers have issued a tough demand that any final agreement include decades of international inspections of Tehran's atomic programme.
"A final agreement with Iran must put in place a long-term inspections and verification regime that lasts at least 20 years," Senate Foreign Relations Committee chairman Robert Menendez and hawkish Republican Senator Lindsey Graham said in a letter they intend to send to Obama this week and were circulating on Tuesday.
The key sticking point in the negotiations is uranium enrichment.
This activity can produce fuel for the country's sole nuclear plant or, if further enriched, the material for an atomic bomb.
Zarif however outlined a possible compromise in an interview with the New York Times published on Tuesday.
This "innovative proposal" would see Iran essentially freeze its enrichment capacities at current levels for between three and seven years.
But Kerry stuck to his guns on Tuesday, saying that nothing short of a reduction in Iran's enrichment capacities was acceptable.
"We have made it crystal clear that the 19,000 (centrifuge enrichment machines) that are currently part of their programme is too many," Kerry said.
The Western diplomat said that Iran's position on enrichment has in fact shifted "very, very, very little" during the recent months of talks.
"An extension appears inevitable at this stage. The parties are neither prepared to sign the dotted line nor to walk away," Ali Vaez, International Crisis Group analyst, told AFP.
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