Morris, whose talismanic presence has been pivotal in the club's upturn in form since early February - which has boosted hopes of a third 'Great Escape' from Championship relegation in the space of less than a decade, came off with 20 minutes to go in Tuesday's 2-0 victory over Bristol City with a calf issue.
Speaking afterwards about Morris, head coach Poya Asbaghi said that the eight-goal striker, who netted the Reds' opener and has found the net in successive home matches, came off as a precaution.
But there were understandable fears that Morris would miss Saturday's trip to Bramall Lane at the very least.
Providing an update on Morris, assistant Ferran Sibili commented: "He will be training tomorrow and then after tomorrow, we will see his reaction. But he will be training tomorrow.
"It does not feel as bad.
"We have no other bad news and people will be ready to train and from there, we will take (name) the squad."
Morris's fellow strikers Cauley Woodrow (knee) and Victor Adeboyejo (cheekbone) remain out of action and will miss the trip to Bramall Lane.
Woodrow has been sidelined since knee surgery in December, but the club are hopeful that he will return before the end of the season - to boost the Reds' survival fight.
Adeboeyjo's last first-team involvement was in the 3-0 loss at Nottingham Forest in late January.
Sibila added: "It is difficult to say a day regarding Cauley for example because of the kind of injury he has. He can take steps forward and then steps back, so it is difficult to say. What I hear from him and everything from the doctors is that everything is progressing how it should be.
"With Victor, we are still following the doctors' advice and he is training without contact."
Meanwhile, Sibila said that there is no issue regarding Josh Benson, who was not involved in the match-day squad for Tuesday's game with Bristol City.
On his non-involvement, the assistant explained: "Because at the end, we have more than 20 players and a lot of players are in and out due to the needs of the game.
"It is difficult for me to answer this as an assistant coach. But Josh is working well, as the other players are. If a player is not plying, it does not mean he is not doing things well. But 11 play (start)."