The former Norwich City frontman, who made an outstanding impact after arriving in January, has been sidelined since mid-August.
Morris injured his knee in the victory over Coventry City at Oakwell on August 14.
He is back training with the group and Laumann has revealed that the target man could, at a push, have an outside chance of even featuring from the bench in Saturday's relegation six-pointer with fellow strugglers Hull City - although a return after the international break is more likely.
On whether he will definitely be back after the break, Laumann said: 'Yes.
"He started quite well in the season and last season, he had a big impact and we are very happy we are looking forward to getting him back.
"He is training with the group and could not start, but could be in the squad and getting some game time and be ready for that. Even this weekend, but we will see.
"At the minute, we are thinking about getting him fully fit after the international break."
Meanwhile, Laumann says that there are no updates regarding his own situation and he is looking no further ahead than Saturday's game.
The Moroccan made an impressive start to life as interim head coach, guiding Barnsley to a first victory in 14 matches in Wednesday's 2-1 victory over Derby County and a second straight win would significantly enhance his own prospects of potentially landing the job on a full-time basis.
Laumann, who will again be without assistant Tonda Eckert, who is still in Covid quarantine, continued: "I do not have any updates.
"We did not really speak about that. I did not ask, it is just to focus on tomorrow and hopefully win the game and then we have a break and we see what happens.
"It would take it if we win tomorrow and we are quite confident. But what happens after that doesn't really matter."