For striker Morton, it would be a second debut following last season's loan spell from West Bromwich Albion.
Brown, who is hopeful of making further signings before the transfer window closes at the end of the month, told The Gazette: “They have been training but I don't know if it's too early .
“Cal will be a fantastic signing and Shaun I know all about (as an opponent in Scottish football). He's great in the dressing room and can be a leader. He won two cups in a season (2020/21 with St Johnstone) and that's the winning mentality I'm looking for.”
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Brown wants lessons to be learned from the opening-day defeat at Port Vale as he looks forward to his first competitive home game as Town boss.
He added: “Plymouth will want to play and have good players, and its about putting them under pressure.
“We have to be brave as we were for 25-30 minutes on Saturday. We want to be possession-based but we need to be calmer on the ball.
“We have to be a bit more ruthless in front of goal and you have to take your chances at this level because we'll be underdogs in a lot games.
“Sometimes it won't be pretty but it's about having that desire and spirit to hold out.
“We spoke about a winning mentality, being brave and holding out when you are 1-0 up,” as Town were at Vale Park before the hosts hit back with two goals in quick succession.
There was again a youthful look to Fleetwood’s line-up and Brown confirmed that giving first-team opportunities to Academy players would continue to be a cornerstone of the club’s strategy, as it was for his predecessors.
"Yes, it's an important part of our focus and it’s something this club is all about,” Brown told The Gazette.
"Bring through talented players from the Under-23s into the first team and help them to make that jump.
"We do make demands of the younger ones and ask if they are ready to make the jump.”