Stones has faced criticism for the first time in his professional career this season, with his performances coming under fire.
The youngster has been accused of making too many errors, but Allardyce feels that the England international would be perfectly suited to playing next to a powerhouse like Kone.
“I’d like to sign Stones, him alongside Kone would be a good combination,” Allardyce said.
Of course, there are no suggestions that Sunderland will actually be launching a bid and the comments were certainly tongue in cheek.
Stones has attracted the attentions of the likes Barcelona and Chelsea recently, and he is tipped to have a career at the highest level awaiting him.
Allardyce says that if he was Stones’ manager, there would be one crucial skill he would look to teach him, though.
“I’d teach him how to defend,” he said. “It would be a simple job for me. That’s my area of expertise in many ways. I can coach in all departments, especially team-play but when it comes to defending, you name it, I’ll tell you about it.
“It wouldn’t be too difficult to show him, a player of his intelligence, when and where to do things."
Sunderland are set to host Everton on Wednesday evening, in what looks a hugely important match.