"He wants to remain in Edmonton and they know that," Smyth's agent Don Meehan told the Journal.
Smyth could be looking for an annual salary higher than $3 million and team management might not be willing to spend as much.
The Oilers could be comparing Smyth's asking price, based on his age and his points this past season, to one-time Oiler Jason Arnott, who is 37.
Arnott agreed to a one-year, $2.5 million contract with the St. Louis Blues, signing as an unrestricted free agent last summer.
Colorado Avalanche captain Milan Hejduk, who is 36 and considering retirement, also signed a one-year, $2.6 million contract this past season, and posted just nine fewer points than Smyth did.
Smyth would most likely be paid for what he can still do on the ice as he could be a third-line winger next season, with powerplay time, and also for playing 852 games as a member of the franchise that selected him in the first round, sixth overall in the 1994 NHL Entry Draft.
In 82 games with the Oilers this season, Smyth collected 19 goals and 27 assists for 46 points, and 82 penalty minutes.