The Toffees' pursuit of a replacement for Ronald Koeman, who was sacked three and a half weeks ago, was expected to have at least gained some momentum, if not actually been sorted, by the end of the global break.
Unsworth, who stepped up after the sacking of Ronald Koeman, stated his intention to keep the job when he was made caretaker, but has lost three of his four games in charge.
"I've seen bits of speculation but not a great deal".
However, with Watford rejecting overtures for their boss Marco Silva, under-23 manager Unsworth is set to continue in the short term. As I've said plenty of times before I'm just getting on with what I do here.
He added: "I have spoken to the chairman every day since I've sat in this role and he has been magnificent".
"This is an wonderful club with the best fans".
"So anybody who would ever rule themselves out of this great job would be a surprise to me".
"For me such a long time without a decision, I had to make a decision myself".
"We will not countenance an approach for our manager, either from Everton or indeed any other club, be it in the Premier League or overseas", a spokesman for the club was quoted as saying by Sky Sports.
The result moved Everton up to 15th place in the table, but they remain just two points clear of the relegation zone and face back-to-back away fixtures against Crystal Palace and Southampton. If not I will shake their hand and wish them all the best because I want them to succeed and I want this club to succeed. You get interest, whether it's me or my players.