Speaking to reporters at the Spanish Formula One Grand Prix, Gourlay also said staying at the West London club's current ground remained Chelsea's preferred option despite a bid for the landmark Battersea Power Station site.
Gourlay was at Barcelona's Circuit de Catalunya to launch the FA Cup winners' new partnership with the Swiss-based Sauber team.
"We have been discussing things with Didier," he said. "Everybody knows he's in the last year of his contract with Chelsea. Ongoing conversations have been held with Didier since January and before.
"Didier loves Chelsea football club, we all love him and we will continue to be in dialogue and we will discuss things after we finish the Champions League final next week."
Drogba, 34, scored in Chelsea's 2-1 Cup final win over Liverpool last weekend to become the first player to score in four finals.
He will be hoping to bring home the Champions League trophy from Munich next week when they play Bayern in the Germans' home stadium.
"We said we would wait until the end of the season and we'd review the situation. That's exactly where we are today and we'll see where we go from there. But he's done a fantastic job and so have the players."
"The club has outgrown Stamford Bridge," he said. "We'd ideally like to stay... we've been looking to extend the stadium to 55,000-60,000.
"That really doesn't appear economically viable at this stage and would cause us a number of planning issues. But we are still looking at overcoming that if we possibly can. The preferred option is to stay at Stamford Bridge."
