The Flames start the season at the Edmonton Oilers on Oct. 12, the opening game at Rogers Place.
"If Johnny happens (signs on Sunday), or whenever it happens, or a week or whatever, we'll deal with that then," Calgary coach Glen Gulutzan said. "But we're just going day by day with the best units on the power play and the best lineup we can put together."
Treliving reportedly met with Gaudreau's agent, Lewis Gross, this week in New York. Reports have said the sides are about $1.5 million apart, with the Flames offering $6.5 million annually and Gaudreau seeking $8 million.
Gaudreau, 23, led the Flames in goals (30) and assists (48) last season and finished tied for sixth in the NHL with 78 points. He has been a restricted free agent since his entry-level contract expired July 1.
Flames center Sean Monahan, who was a restricted free agent, signed a seven-year contract with a reported average annual value of $6.375 million on Aug. 19. Gaudreau and Monahan have been linemates for the past two seasons, combining for 112 goals and 267 points.
A fourth-round pick (No. 104) at the 2011 NHL Draft, Gaudreau has 143 points (55 goals) in 160 NHL games and has the sixth-best point-per-game average (0.89) in the League since the 2014-15 season.