The 44-year-old Unsworth was named as caretaker after Ronald Koeman was sacked at the beginning of last week, but has seen his side lose both of his games in charge,Chelsea at Stamford Bridge in the Carabao Cup and to Leicester City in the Premier League.
The Toffees face Lyon on Thursday night (2 November) in the Europa League as they seek to keep their slim hopes of qualification alive, before hosting Watford at Goodison Park on Sunday afternoon.
A host of managers are linked to the vacant post on Mersesyside and while chairman Bill Kenwright is understood to be keen to see Unsworth given the opportunity to land the job permanently, the club's majority shareholder Farhad Moshiri is determined to bring in a more high-profile replacement for Koeman.
Consequently, Unsworth has reportedly been given the next two fixtures to prove he can land the job on a permanent basis, but the former Everton defender insisted he was not fazed by the task.
"That doesn't scare me, because I know the game, and I know that in the end you will be judged, I know, on performances – and I think performances have improved for a game and a half, certainly in the second half against Leicester," he was quoted as saying by the Liverpool Echo.
"But within those performances, you've got to try and dig out some results, so I want to win the game tomorrow, I want to perform, and Sunday's a massive game as well.
"Sunday's a cup final for me and I think we've got to play it like a cup final, I certainly want the players to play it like a cup final."
Tuchel and Ancelotti would both be available to start immediately but the former is reportedly keeping an eye on the Bayern Munich job, given caretaker manager Jupp Heynckes will leave Bavaria at the end of the season.
Silva, meanwhile, is thought to be Moshiri's preferred option but appeared to rule himself out of the running earlier this week, when he insisted he remained committed to his role at Vicarage Road.
However, Unsworth insisted he was not concerned about his future.
"I've not picked up a newspaper, because I haven't had time, honestly!" he said.
"I wouldn't know who was in the running for [the manager's job]. I've heard certain things, but it's a top job, and I'm not surprised with whoever would be linked with it.
"It's football and I get football and I know football."
Everton have picked up just one point from their first three Europa League games this season and trail second-placed Lyon by four points. Unsworth, who has left Wayne Rooney, Phil Jagielka and Leighton Baines back in Liverpool, believes his side are good enough to secure their first win in all competitions since 23 September.
"None of us have a crystal ball, and none of us can predict," he said when asked whether he would not be tempted into playing his strongest XI.
"I've brought a squad here who I believe in. I know my team already, and I think it's a team that can challenge and get a result."