Morais picked up a knee injury in training on Monday and Parkinson admits that unfortunately the initial diagnosis doesn't look good.
The Portuguese winger will have a scan on his injured knee this Wednesday but the City chief says he is expecting the worst.
He said: "It is a big blow for us.
"Yesterday (Monday) was a low day down at the training ground given that one of our key players had just got injured.
"We have a scan for Filipe tomorrow (Wednesday) but we are obviously fearing the worst.
"We will keep our fingers crossed, however, it isn't as bad as it first looks."
The news of Morais' injury concern came after a 2-1 defeat for City at Guiseley's Nethermoor.
In a much-changed Bradford squad for the friendly, nine trialists and five scholars featured in total for Parkinson's side throughout the night.
Recent recruits Jon Lewis, Luke James and Mark Marshall all featured as well though, with the trio catching the eye of the plentiful City support within the ground on the night.
Parkinson added: "It was a great pitch to play on and a great attendance in the ground.
"I felt we did well if you look at the team we put out. We certainly had very little time to work with that team.
"It was a creditable display and result from the lads when you consider that Guiseley had a strong team out.
"It was only really in the second period when we made changes that we started to look a bit vulnerable at the back.
"Looking at the performance of our forward players, I think both of their centre backs would have been sent off if this had been a league fixture.
"The ref was lenient as this is pre-season but those three (Lewis, Marshall, James) looked sharp.
"We will move on from this game now and continue to try and get some more players into this squad."
Speaking after the Guiseley game, Parkinson revealed that a trip to Whitby Town next Tuesday will now also be a part of City's pre-season schedule.
He added: "We are looking at Steve (Davies), he is back in training this week, and we are thinking that by that stage it might be a good opportunity for him to get some game time.
"With that in mind , among other things, we felt we needed to add another fixture to our pre-season."