Engelaar impressed in a holding role for the Dutch before Marco van Basten's side lost to Russia in Saturday's quarter-final.
The 28-year-old is looking to leave Twente over the summer and has already agreed personal terms to join former
coach Fred Rutten at Schalke.
However, the two clubs have yet to agree a fee and the Toffees and Magpies are monitoring the situation.
The player is looking to hold talks about his future this week and hopes Twente will not reverse their decision to allow him to leave.
"I want there to be clarity," Engelaar told RTV Oost. "And that will come this week. I think it will go okay, I do hope so.
"I won't play at Twente with anger in my body, I am not like that, but somewhere different is nice.
"I just want to make the move and we have made clear agreements about that with Twente. It would be a pity if they don't want to keep to that now."