Roberto Martinez’s side have lost just once in the opening 15 games of the new Premier League season and, after winning at Old Trafford and drawing at the Emirates Stadium, sit in fifth place.
Osman has featured in each of the Toffees' league fixtures this term, including an appearance off the bench in Sunday's 1-1 draw with Arsenal, and is confident the Merseyside outfit can maintain their form.
|5/1||Everton are 5/1 with BetVictor to finish in the top four|
"We always came positive and wanting to win, but maybe there is a bit more belief now - however, we are not going to get ahead of ourselves.
"We have had a good week, but everyone knows things can change quickly. We will hopefully keep ticking along quietly and see where that takes us."
The Toffees are currently on an eight-game unbeaten run, and manager Martinez is thrilled with the way his side have matched some of the league's more dominant sides in recent weeks.
"At the moment, we are so focused on how we are trying to play that the next six months is going to be great potential for us as football club," the Spaniard said.
"We went to Manchester City earlier in the season and could not be ourselves, to play the way we wanted, and consequently we lost the game.
"Since then we went to Old Trafford and the Emirates in the space of a week and it was a completely different performance and that was an incredible sign.
"We have a blend which excites me and all the players are working hard trying to improve and develop. I am really excited about the potential of these group of players."