"It's hard to be [optimistic] at this point, to be honest," Anthopoulos said Wednesday. "We're still not sure with him when he's coming back.
"Morrow still isn't feeling right. So we're going to get him examined again. We've gotten MRI's done before, but he just doesn't feel 100 percent."
Morrow has been on the disabled list since June 1, and has not pitched for the club since leaving two innings into his start against Atlanta on May 28.
The 28-year-old right-hander last threw in a game with Class A Dunedin on June 17, and was shut down with the same issue. He was supposedly feeling better and had begun throwing side sessions two weeks ago, but the soreness in his forearm continues to linger.
"We're going to give him a little more rest," Anthopoulos said. "It's one of those things it might just need rest. He's a lot better than he was, and he feels better, but he still doesn't feel like it's 100 percent.
"The odd part is that we've taken MRIs, we've done all those type of things, and we haven't been able to pinpoint anything other than inflammation. It might be one of those things that it just needs a lot more time than we hoped and thought."
Morrow has only made 10 starts this season with Toronto, and his current ailment is his second battle with health problems this year, after dealing with upper back and neck tightness earlier.
Health has always been the biggest issue for Morrow, who started the year as the club's No. 2 starter. This marks the fourth consecutive year in which he has spent some time on the disabled list since joining the Blue Jays in 2010.