Morris, signed in the summer after leaving Scunthorpe, was carried off on a stretcher in the first half of Friday night's 1-0 win at Highbury after going in for a challenge with North End's Darnell Fisher.
Ash Hunter, who came of the bench to replace him, scored the winner in the second half.
Barton said: "Hopefully Josh Morris going off was more precautionary than an injury because it would be a blow to lose him, he's been excellent since he's been at the club.
"We won't know until it's X-rayed. I went in to see Josh at half-time and he said he did want to walk off the pitch but the medical team were on the safer side.
"Fingers crossed in the next 24 hours we get some good news."
Fleetwood were worthy of their victory which capped off a pleasing pre-season programme.
Barton said: "We had been a shade unfortunate to lose to Burnley on Tuesday night and probably played the best stuff of my tenure in the first half against them.
"We asked the lads to back that up against Preston. I thought we started really brightly and then Preston with the quality they had, came back into the game.
"I made a couple of adjustments at half-time and I thought second half we were superb, probably a tad unfortunate not to win by a more comfortable margin.
"With a bit more composure in the final third we could have done that but it was a really good work out for us which ends a good pre-season.
"We did a lot of things right, there were just a couple of triggers we need to work on.
"Preston switched the play quickly which good players do, that negated the pressure we were trying to apply to them.
"We tweaked that at half-time but it is still relatively new to a couple of the lads.
"It will take time and effort on the training ground.
"In the second half we adjusted and limited them to a pot shot from 25 yards which the young goalkeeper gobbled up."
Fleetwood start their League One campaign with a visit to Peterborough United next Saturday.