The Magpies are still looking for a new manager after dismissing Steve Bruce a fortnight ago.
Emery has emerged as a frontrunner for the Newcastle job but his reported €6m release clause will have to be defrayed before negotiations can begin.
Newcastle have emerged as one of the richest clubs in the world overnight following a £305m takeover by Saudi Arabia’s Public Investment Fund.
Emery had an 18-month spell in charge of Arsenal in his previous role.
The 50-year-old led Villarreal to a 2-0 win over Young Boys in the UEFA Champions League on Tuesday and the former Sevilla and Paris Saint Germain manager confirmed Newcastle’s interest afterwards.
"The truth is that they have shown an interest in me, but I have no further news," Emery said during his post-game news conference. "There is no offer. There have been no more steps.
"I am focused on Villarreal. It will have to be a contact between clubs. My idea is to be here on Sunday."
"Well, first I would talk to the president. I neither close the door nor open it to Newcastle," said Emery, who won three successive Europa League titles with Sevilla before leaving for Paris Saint-Germain in 2016.
"I have not said no, but I would discuss it with Villarreal. I am very grateful. I cannot say anything more. We have already talked about noise. The first one who is uncomfortable is me, but we have been focused on the game."
Emery won the Europa League with Villarreal last season, beating Manchester United on penalties after a 1-1 draw.
