Di Matteo needs to see he has sufficient match sharpness for the home meeting with Harry Redknapp's side.
The Baggies boss said: "Paul is in good shape physically but we have to see how his match fitness is.
"Tomorrow we have a reserve game and we will give him some time on the pitch."
Di Matteo admitted he has recruited Scharner primarily to operate in midfield even though he can also play at centre-half.
He said: "I said to him I was recruiting him as a midfielder. We know he can play centre-half but primarily he has been signed as a midfielder."