Jens Keller is currently calling the shots in Gelsenkirchen, but his contract only runs until the end of the campaign.
Despite being praised for the work he has done since replacing Huub Stevens in December, Keller is not understood to be a leading candidate to keep the job full-time, even if he succeeds in leading the club into the Champions League.
Effenberg's name was doing the rounds at the weekend and Heldt was non-committal when asked to comment on his club's link with the former Borussia Monchengladbach and Bayern Munich midfielder.
"I don't really have to say too much about it," he told Sky television.
"Everybody has a right to speculate about who will be our future coach, but all I can say for certain is that nothing has been decided yet.
"I see Stefan often and I cannot deny that I have met up with him because he works for Sky.
"Stefan was an excellent footballer and I like to listen to him - he is always knowledgeable, well spoken and never controversial.
"He has been incredibly successful in his career and he is certainly going to be a great coach in the future.
"Only time will tell what Stefan does. We are the ones who can determine when we announce our decision."
Sunday's 4-1 win over Hamburg lifted the Royal Blues three points clear of fifth-placed Eintracht Frankfurt and also boosted their goal difference in the race for the Bundesliga's fourth Champions League berth.
Effenberg, who has a coaching badge but has never worked in such a capacity, could therefore debut at the very top of his trade next season.
And he has not ruled out the idea.
"My aim is to be a coach aiming for success," he said. "That is possible with Schalke, but also elsewhere."