According to a source within the Celtic camp, the technical team has requested to assess the Kaizer Chiefs striker before he can sign on the dotted line.
Mthembu left Naturena for Bloemfotein earlier this week hoping to conclude the deal, but he was told he needed to impress caretaker coach Lehlohlonolo Seema first.
"He's been asked to train with the first team so that he can be assessed properly, and for that reason the deal hasn't been finalised," the source told Goal.
"If the technical team is happy with what he can offer then he will sign," the source added.
The 29-year-old hasn't kicked a ball this season, although he made a few appearances for Amakhosi in the MultiChoice Diski Challenge, his level of fitness is still a concern.
His future looked bleak at the end of last season after he was placed on the transfer list, only to be given a second chance by the Amakhosi management at the start of the 2016/17 campaign.
However, he struggled to win a place in the team, and as Goal reported in November, it was decided that he would either be offloaded in the current transfer window or his contract would not be renewed in June.
As things stand, Mthembu is still a Chiefs player and if he fails to secure a move away from the club before the end of this month, he will leave the Soweto giants for free come July 2017.