The group has since held talks with a view to buying Conference side Kettering Town.
Smith said: "These talks were covered by a confidentiality agreement, but in view of press reports we consider we are honour bound to clarify the matter for supporters.
"Talks took place between the club and a consortium who wanted to buy a controlling interest in Port Vale. This consortium were also having similar discussions with a number of other clubs.
"We understood that one of the conditions was that Gascoigne became team manager, this was unacceptable because of our confidence in and loyalty to the current management team.
"The acid test when considering any takeover bid is that it is in the best interests of Port Vale. Suffice to say that the talks did not progress and the consortium has moved on elsewhere."