Ms Simpson told the Herald she met Mr Goff on September 30 at a cafe in Remuera to discuss local matters.
Hand on heart, she said, the deputy mayor's role was "never, ever discussed".
She said she would like to stand for the Orakei ward on council if sitting councillor Cameron Brewer steps down.
Mr Brewer is widely expected to step down next year to focus on a new PR business venture and a new, young family.
Mr Goff said he had not given any thought to a deputy mayor if he did decide to run for the mayoralty.
"The very worst thing you could do in the position of being a candidate would be to make promises to this group or to that group," he said.
Mr Goff, who two weeks ago told the Herald he was "likely" to run for the Super City and make an announcement before Christmas, is now expected to declare his hand next month.
He said he had not discussed standing for the Super City with Mayor Len Brown, who is also a member of the Labour Party.
Mr Brown, who is being urged by allies to step down after a second term marred by revelations of an affair with a council adviser, has not said if he will seek a third term.
"If I do stand I will probably give him (Mr Brown) a phone call beforehand," Mr Goff said.