The 29-year-old striker joined Everton in January on a short term deal until the end of the season, but has been struggling to get game time at Goodison Park.
He has made eight appearances from the bench for Everton since joining the club and is still waiting for a start under Carlo Ancelotti.
The Everton boss is unlikely to drop Dominic Calvert-Lewin, while Richarlison also remains a key part of his plans, which has left King waiting for his opportunity on the bench.
It has been claimed that several clubs are interested in him ahead of the summer and are monitoring his situation at Everton.
They are prepared to pounce if his frustrations at Goodison Park continue, but King himself is keen on a longer stay at Everton.
He wants to prove himself to Ancelotti and earn a longer team deal at Everton over a move to another club.
The 29-year-old is desperate to get an opportunity to start and show Ancelotti that he is good enough to lead the line at Everton.
It remains to be seen whether he does enough until the end of the season to earn another contract at Goodison Park.
