The three-time American League MVP has not played since May 17 after going on the injured list with a right calf strain. The original prognosis was six to eight weeks, but Trout has been out of the lineup for 12 weeks since sustaining the injury.
Wednesday marked the 75th game that Trout missed, which is his longest stint of missed games in his 11-year career. Trout's progress stalled after he felt some discomfort after a couple of days of running the bases a couple of weeks ago.
Scans showed that the calf is continuing to heal, albeit slower than anticipated.
"My policy with any player is we go day-to-day and communicate," Minasian said before a 10-2 loss to the Toronto Blue Jays on Wednesday. "From our end, we will not rush him. We want him to feel good about how his calf feels and to play at his level when he does come back."
The Angels are 57-58 this season and are 39-36 without the All-Star slugger.
Trout, who turned 30 on Saturday, went on the injured list May 18 after he came up limping while running between second and third base during the first inning against Cleveland.
When he got hurt, Trout was leading the majors with a .466 on-base percentage. He was batting .333 with eight homers and 18 RBIs in 36 games.
"You want to go into those offseason months knowing that, 'Hey, I played again, I felt good, everything's fine,'" Angels manager Joe Maddon said. "So that's always part of it, too."
The Associated Press contributed to this report.