The 26-year old centre-back is a free agent after leaving Wolves recently and is expected to sign a one-year deal with the Hoops after undergoing a medical.
Mouyokolo got through 90 minutes in a bounce match against Ukrainian side Sevastopol in Germany on Wednesday night and Celtic boss Neil Lennon was positive about the potential signing.
"I thought that Steven was really good considering he hadn't played for such a long time. We have liked him for a long time. He's had a few injury problems but has come on trial and impressed us," he said.
"Things have been agreed more or less in terms of a contract.
"He's done a medical and we're just waiting on the reports coming back.
"If everything is okay, we'll go ahead with it. Hopefully we will get it finalised this week."