Zuma responded to Mentor's allegation only a few days after it was reported that Deputy Finance Minister Mcebisi Jonas was offered a ministerial position by the Gupta family late last year.
The Sunday Times reported at the weekend that Jonas turned down an offer by the Guptas to have him appointed finance minister a week before Nhlanhla Nene was fired from that position.
Nene was replaced by David van Rooyen, who was replaced by Pravin Gordhan four days later.
Last night Zuma said he was unable to comment on the allegations made by Mentor.
"President Jacob Zuma has no recollection of Ms Mentor," read a statement from the Presidency.
But records show that Mentor accompanied Zuma on a trip to China in 2010. Late last night, his office said Mentor was ''definitely not part of the official delegation''.
Writing on Facebook yesterday, Mentor claimed that, in 2010, the Guptas offered her the post of minister of public enterprises on condition that she would then end SAA flights to India and award the route to the family instead.
"I refused and so was never made a minister," she wrote.
She claimed that Zuma was present when the offer was made.
"The president was in another room when they offered this to me [at their home] in Saxonwold.''
Two weeks ago, the ANC's top six office bearers met the Gupta family following complaints from party members and its alliance partners.
Solly Mapaila, the SA Communist Party's second deputy general secretary, openly complained about the influence of the Guptas on the governance of the state.
He has called for a judicial commission to investigate the relationship between the government and the Guptas.
The family has previously been linked to the appointment of Sport Minister Fikile Mbalula, Mineral Resources Minister Mosebenzi Zwane and Van Rooyen. Both Zwane and Van Rooyen have denied allegations linking them to the Guptas.
Yesterday the Gupta family dismissed Mentor's allegations and challenged her to put her accusations into a sworn affidavit.
"No meeting has ever taken place between Vytjie Mentor and any member of the Gupta family or their representatives, and no job offer was made," the family said.
"Facebook is not the appropriate forum to air such a complaint, and we can only assume it is an attempt to gain personal profile and media attention."
ANC members yesterday demanded answers from their leadership. The Guptas' influence on the state is likely to dominate proceedings at the ruling party's national executive committee meeting later this week.
Political analyst Ralph Mathekga said evidence of the Guptas' influence on the state and on the country's political machinery did not matter.
"The fact of the matter is that the Guptas are not doing anything illegal. They are simply using their network of influence," he said.
"We are too preoccupied with peripheral issues when we should rather be concerned with the extent to which the ANC, the state and the entire party political machinery have been captured by the Guptas.
"Zuma is merely the weak link in this matter but we need to find out how much of the state machinery they have captured. If much of it has been captured, we must certainly be very worried.
"We cannot treat the ANC as a victim" because it is "party to this".
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