Mack was absent from the team's first day of mandatory minicamp on Tuesday as he seeks a lucrative contract extension, per multiple media outlets.
A three-time Pro Bowl selection and 2016 NFL Defensive Player of the Year, Mack is set to make $13.846 million this season in the fifth-year option of his rookie contract. The 27-year-old reportedly is looking to become among the highest-paid non-quarterbacks in the league.
"I don't know; I just hope so," Gruden said of the team finding common ground with Mack, via the Raiders' official website. "One of the big reasons I came here was to coach that man, but I don't want to speculate. There's a lot of guys in the league, several players that are in a similar situation, and we're just trying to resolve it as soon as possible.
"In the meantime, we'll coach the players that are here."
Mack is subject to being fined up to $84,435 for missing the entire minicamp, although Gruden was not interested in addressing that topic.
"I just move on with the questions," Gruden told reporters. "I'm not going to get into what we're going to do. That's our business, honestly, and we'll deal with it accordingly. We're hoping to get the man signed and I'll leave it at that."
Mack recorded 78 tackles and 10.5 sacks in 16 games last season. He has 303 tackles and 40.5 sacks in 64 career contests since being selected by the Raiders with the fifth overall pick of the 2014 NFL Draft.