The Toffees have splashed the cash on the likes of Davy Klaassen, Wayne Rooney, Jordan Pickford and Michael Keane this summer.
They have let Romelu Lukaku join Manchester United but are still pondering whether to reinvest that cash in Gylfi Sigurdsson.
Everton have already had one bid rejected by Swansea, who are holding out for £50million.
Asked if Everton could finish above Liverpool this season, Osman said: “Absolutely. The divide isn’t that big with regard to the league.
“I think Everton seem to be not capable of beating Liverpool enough times when it’s head to head.
“But, over the course of the season points-wise, there isn’t much in it.
“A top six and improving is the aim and any kind of silverware. Everton have waited a long time.
“They say you get the first one and more will follow. Everton are desperate for that at the moment.”
