Keene spent the past week trying to win the favour of head coach Gavin Hunt at Sturrock Park.
The 29-year-old has since returned home. However, there are indications he could return.
"He has since gone back home. We will make the statement in due course," Wits CEO Jose Ferreira tells KickOff.com.
"Yes, he did well."
Keene had an assessment with Kaizer Chiefs in March last season but a move failed to materialise.