The multistep reconciliation process includes the United States reintroducing waivers on eight countries buying Iranian oil, the channel has reported.
It was also told by its source that the rivals had not taken steps so far to soften their stance but a French presidential adviser had been given the green light to continue efforts to "revitalize" the nuclear pact.
The EU Foreign Affairs Council held a meeting in Brussels on Monday to discuss the Iran nuclear deal in the wake of Tehran's recent decision to partially abandon its nuclear obligations under the 2015 accord.
Iran was encouraged to immediately come into full compliance with the 2015 nuclear treaty and use its leverage on militant groups in Iraq, Syria and Yemen to stop them from attacking US allies.
The IAEA international nuclear watchdog confirmed last week that Iran had enriched uranium beyond the agreed level. Iran said it would continue ramping up enrichment if other signatories did not shield it from US sanctions. They snapped back into place after Washington quit the deal last year.