The England U-21 international has spent the last two seasons on loan with Aston Villa and Charlton respectively.
Portsmouth had been hoping to sign him on a similar deal but have been told he wants to stay at Chelsea.
Portsmouth chairman Milan Mandaric admitted to Sky Sports that the move for Cole has been put on ice with the player putting his Chelsea ambitions first.
“Carlton would select us after Chelsea but he wants to give himself a chance at Chelsea first,” said Mandaric.
Good news.
