Davenport was paid off by former club West Ham but is still unable to train due to the incident back in August which saw him suffer knife wounds to both legs.
Speaking to West Brom's official website, the Baggies boss said: "We're waiting for him to get in a better position and maybe come in. "The position is still the same. He's still not in a position to be able to train. He was around the place last week but not this week. We are in touch.
"It's a possibility to look at him, see how he is, and for him to get some training as well."