Nathangelo Markelo has been challenged to deliver consistent performances to keep alive hopes of a new contract.
The 21-year-old midfielder's deal is up this summer but it is understood the Blues have the option of extending it by an extra 12 months.
Markelo is a mainstay in Everton's under-23s and was a key part of their Premier League 2 title success last term.
Industrious Everton youngster leaves Marcel Brands with transfer conundrum
On Friday night, the young Dutch player impressed against leaders Chelsea in a 2-2 draw and David Unsworth says he will give himself a great chance of earning a new deal if he maintains those standards.
"I thought Nathan was terrific tonight, we've moved him to more central of the three role," he said.
"He's different to Beni [Baningime], Beni will take it off the back players. Nathan is a great presser of the ball and sets things off. We've worked on that this week and, apart from the kick-off for the second-half, that's probably his best game for us this year.
"If he were to put 10 games, like that, back-to-back, I'm sure Marcel would be getting a lot of phone calls about him."
Markelo was signed from Volendam in the summer of 2017 and Unsworth added: "When he performs like that you wouldn't want to let him go and he'd be a massive asset but it's really down to him, and his performances, what the future holds."
