Mularkey told the Florida Times-Union that he hasn't been in contact with Jones-Drew, who skipped the club's entire offseason program because of his displeasure with his contract situation.
Jones-Drew, who led the NFL in rushing last season with 1,606 yards, has two years remaining on a five-year contract worth $31 million. He is scheduled to make $4.45 million this season and $4.95 million in 2013.
Mularkey declined to tell the newspaper whether he will impose a $30,000-a-day fine if Jones-Drew does not report starting Thursday. The dollar figure is the maximum allowable fine for signed players who miss camp.
Coming off a career year, Jones-Drew wants to be one of the league's highest-paid backs. His contract currently ranks eighth among NFL backs behind Minnesota's Adrian Peterson, Tennessee's Chris Johnson, Philadelphia's LeSean McCoy, Houston's Arian Foster, St. Louis' Steven Jackson, Carolina's DeAngelo Williams and Seattle's Marshawn Lynch.
General manager Gene Smith said during minicamp in June that the team has no plans to renegotiate with Jones-Drew, setting the stage for a potentially lengthy holdout.
Information from The Associated Press was used in this report.