Fabbrini, who is on loan from Championship rivals Watford, was expected to make his Blues debut over the Easter period but suffered a broken nose in training.
However, manager Gary Rowett has confirmed the Italian forward could play in the home game against Wolves wearing a protective mask.
"It was a bit of a blow. He broke his nose in training on Sunday," Rowett told the club's official website.
"Diego went back to Italy. Hopefully we will be able to get a mask fitted for him and then he will come into contention, potentially, for the weekend.
"We will see what the specialist says."