"It's up to Josh as to when the discussion will take place," Fowler said. "We've given Josh what we think the range will be.
"We want him here. … It's a priority to keep him here."
To date, the Padres and Headley's representation have not had significant discussions about a long-term deal.
Headley, who is coming off one of the best all-around years in franchise history, won't be eligible for free agency until after the 2014 season. Headley won his first Gold Glove and Silver Slugger awards and finished fifth in the National League MVP vote in 2012.
Fowler declined to speculate on the expected annual value the Padres will offer Headley, but he did say the deal won't cover 10 years. Headley is making $8.575 million this season and is the second-highest paid player on the team behind left fielder Carlos Quentin ($9.5 million). It has been suggested that he will receive around $15 million annually.
"I made the comment that he would be the highest-paid player in club history," Fowler said. "I stand by that comment. But where the [$15 million per year] number came from … some reporter had it in the paper. I said something to the effect in that range, but we're not going to get into those numbers [publicly]."
Just one month after winning the 2007 NL Cy Young Award, pitcher Jake Peavy agreed to a four-year deal worth $52 million, which remains the largest contract in franchise history. Peavy made $11 million in the second year of that deal but was traded that July to the White Sox.
The Peavy deal surpassed the four-year, $34 million contract Phil Nevin signed in 2001.
Headley, who missed the first 14 games of the season while recovering from a fractured tip of his left thumb, went 2-for-4 with an RBI and a run scored in the Padres' 6-2 loss to the Cubs on Wednesday in Chicago. He's hitting .280 with six RBIs in 13 games.
Last season, Headley -- who has been with the organization since he was selected in the second round of the 2005 Draft -- hit a career-high 31 home runs and led the NL with 115 RBIs.
Fowler was asked by MLB.com if he had a chance to reach out to Headley after his comments were made public on Wednesday.
"I did not have a chance to, no," Fowler said. "But if there's any misunderstanding or concern, we'll make sure and talk to the right people. We'll get it handled."
Headley declined to comment on the situation after the game.