Lampard's Chelsea contract runs out at the end of the season when he would be free to leave Stamford Bridge after 12 years.
It was reported in some outlets on Tuesday that Gourlay had suggested talks with the 34-year-old midfielder had begun over a new deal, but the club quickly claimed he had been misquoted before posting his comments on their official website.
Speaking at a press conference to promote a forthcoming pre-season trip to Asia, Gourlay refused to confirm or deny talks with Lampard.
"I am not prepared to discuss this (Lampard's future) at this time," he said.
"Obviously conversations must remain confidential between the club and the players at all times so that is as much as I can say."
Chelsea have previously refused to talk about any possible discussions with their players, including Lampard, and remained tight-lipped on Tuesday.
Lampard's potential exit is one of a couple of off-field issues to overshadow the club as the season enters its final quarter.
Interim manager Rafael Benitez confirmed last week that his tumultuous spell in charge would come to an end at the end of the season, with some speculation he may go before then.
While Chelsea's fans have shown their desire to see Benitez leave, the opposite is true of Lampard, following his glittering career in west London.
He is just one strike away from becoming only the second Chelsea player to score 200 goals for the club and is three behind Bobby Tambling's overall club record.
Lampard's agent Steve Kutner claimed in January that the club had told him and the midfielder that he would "not be offered a contract under any circumstances".
Despite that, Lampard has remained a key part of the Blues' first team this season.
The England international has scored 13 goals in all competitions, despite playing a more withdrawn role, as the Blues continue to compete on three fronts.
Chelsea currently sit fourth in the Barclays Premier League, the final Champions League qualification place, while they are alive in both the FA Cup and Europa League.
At present Lampard is free to talk with other clubs about a move, with Major League Soccer side the Los Angeles Galaxy previously linked with the player, although no offers have been made public.