Iranian state media reported on Sunday that Supreme Leader Ayatollah Ali Khamenei pardoned about 700 prisoners, but Esmaili said Zakka's name was not on the list of those pardoned.
On the other end of the line, a source familiar with the case had told the Beirut-based Daily Star on Saturday that Zakka would arrive in Beirut within 48 hours.
Neither the Lebanese government nor Mr Zakka's family have made any mention of Hezbollah's role in mediation and the photos with Maj Gen Ibrahim appear to contradict the Fars report.
Zakka was arrested during a trip to Iran in 2015 on charge of having "deep links" to USA intelligence services.
A top Lebanese security official is in Tehran to secure Zakka's release, which has been anticipated in recent days.
"The release of Nizar Zakka will take place on Tuesday after the completion of the judicial proceedings, which are almost done", Ibrahim said.
In 2016, Iran sentenced Zakka to 10 years in prison.
Zakka, who also has permanent USA residency, had been invited to Iran by a government official in 2015 but then disappeared after attending a conference in Tehran. "This is done exclusively because of the respect for and dignity of [Hezbollah leader] Hassan Nasrallah", the source told Fars. Hezbollah is the most powerful armed force in Lebanon as well as being part of the governing coalition in Beirut.
At the time of his arrest, state television in Iran charged Zakka had "deep ties to military and intelligence services of the United States", Iran's arch-foe. He had just attended a conference there on the invitation of one of the country's vice presidents.
The U.S. State Department said he was being held unjustly and in 2016 called for his release.
A State Department spokesman said on the condition of anonymity that the matter is between Lebanon and Iran.
State media reported in 2017 that he had lost an appeal against his conviction. His potential release comes as tensions between Iran and the US remain high after President Donald Trump unilaterally withdrew America from Tehran's nuclear deal with world powers. However, U.S. -Iranian tensions have risen anew since Washington pulled out of the nuclear pact in 2018.