A source within the NFL said Sparano is "certain" to be coaching the team Oct. 17 against the New York Jets, the Sun Sentinel reported Sunday.
Since winning 15 of his first 21 games as Dolphins coach, Sparano has seen his team descend into an NFL-worst seven-game losing streak dating to last season.
Team officials have said nothing about a possible search for a new coach.
"People are going to speculate," veteran Dolphins linebacker Jason Taylor said. "It's out of our hands. It's not something we have control over. We obviously hope it doesn't happen."
Taylor was asked how Sparano is holding up amid national rumors concerning on his job status.
"He's a fighter," Taylor said. "Obviously, I think the things he's been through since January, he's a fighter and he's shown that.
"He's a hard-headed fighter. That's what football guys should be. He's a football guy through and through."