The Ghanaian utility player began training with the reigning PSL champions last month despite being contracted to Swedish second division side Helsingborgs.
Recent media reports suggest that Gyimah has impressed the Wits technical team and that the club is now keen to sign him ahead of the January transfer window.
When contacted by Goal, Wits' long-serving administrator George Mogotsi said he wasn't aware of the news circulating in the media that Gyimah had already agreed a deal with the Students.
"It's not clear at this stage [whether he will be signed or not]. As soon as it becomes clear, then we will definitely let you know," Mogotsi told Goal.
"He came in and requested to train with the team. Remember, he previously worked with Gavin [at SuperSport United]. He's still training with the team. I don't know anything about him agreeing to a deal with us," he said.
Asked if Gyimah has made a significant progress since he started training with the club in mid-November, Mogotsi said: "He's a quality player."
Mogotsi promised to have something concrete regarding the future of Gyimah at Wits in the next 24 hours.
"Give me until tomorrow then I will give you something concrete, but for now, I have no idea where the news [of Gyimah joining Wits] are coming from," he concluded.
The newly crowned Telkom Knockout Cup champions have one available foreign spot left for the season, meaning they can be able to sign and register Gyimah with the PSL for the second half of the season.
English striker James Keene, Malawian forward Hellings Mhango, Egypt international Amr Gamal and Serbian defender Slavko Damjanovic are the four foreigners, who are currently on the books of the Clever Boys.
Gerald Phiri Jr was registered as a local in May 2016 after receiving his South African permanent residence permit.