British entrepreneur Jones claimed that he couldn't imagine anyone other than Sugar hiring and firing in the famous TV boardroom.
"I think it would be very hard to fill Alan's boots. Never say never, but I just can't imagine anybody else being in that position other than Alan," Jones told Digital Spy.
"He does it so well, that show is really him. I wouldn't be surprised if they stopped the show if he decided he didn't want to do it anymore."
Jones's Dragons co-star Meaden was more coy about the opportunity, teasing: "Oh, I'd wait to see if I was asked. How diplomatic am I?
"So far my gut has led me to the right place in life and at that time, if that question was posed, I would know whether I would or I wouldn't... I've got loads more diplomatic answers if you want them."
Lord Sugar recently downplayed rumours that he may quit The Apprentice after next year's 10th series. "If the BBC decide to do more after next year, I'll do it for them," said Sugar.
Dragons' Den returns for an 11th series in August on BBC Two.
Meaden and Jones will be joined on the new series by show regular Duncan Bannatyne and newcomers Kelly Hoppen and Piers Linney.