The Portuguese, who replaced Sam Allardyce in May, has gone unbeaten this season with four draws. The Toffees currently sit in seventh place.
And Silva wants to create a legacy with the Merseyside club.
"When you're at a club like Everton you want to be a part of that story," said Silva. "For me it's really important - it's a long-term project.
"I want to build something but at the end of the day the most important thing will be the result. Football is always like that but what you want to do in the future is to be part of this big story."