United triggered a one-year extension in the 30-year-old's contract at the start of the year, but agreeing a deal beyond the end of the current campaign is proving difficult.
When asked if he was concerned about the uncertainty surrounding Fellaini's future, Mourinho replied: "Yes, I am."
The decision, however, is out of the Portuguese manager's hands.
"It's a discussion between the player and the board -- I'm not involved in contracts or deals -- and I respect both," Mourinho said.
"I respect the player because the player has the right to decide his future when he finishes his contract. And I respect the board because the decisions are not in my control. I adjust to it, wishing that they have an understanding."
Mourinho confirmed that United defenders Eric Bailly and Phil Jones will miss Saturday's Premier League visit of Brighton and Hove Albion through injury.
Bailly picked up a knock this month and has missed United's past two fixtures, while Jones aggravated a thigh problem on England duty during the international break.
"Bailly and Jones, they are out, but we are okay because we have (Chris) Smalling, (Marcos) Rojo and (Victor) Lindelof," the manager added.
United are second in the Premier League behind rivals Manchester City, who are eight points clear at the top and unbeaten after 12 league matches. However, Mourinho shrugged off concerns over the gap between the two clubs.
"We cannot think about the gap to City, we cannot think about the gap to fifth position. We just have to focus on ourselves," he said.
"We haven't yet reached 50 percent of the season, so let's be calm. We have four competitions to play. Let's go step by step."
(Reporting by Hardik Vyas in Bengaluru; Editing by David Goodman)
