The 18-year-old had looked like he was on the verge of joining Wigan after they had a bid accepted for the defender earlier on deadline day.
However, Everton have now enterted the race for Stones and they have had an undisclosed offer accepted by Barnsley.
Everton boss David Moyes has been searching for a new defender and Stones has been his top target.
Stones is now set to meet with Everton to discuss a move to Goodison Park and undergo a medical.
Moyes has been looking to bolster his defensive options and Stones will give him options at both full-back and centre-half if Everton secure his signature before the 11pm deadline.
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