O'Neill has monitored Davies for several months and his scouts watched the England under-21 player in action for the Baggies against Heerenveen at the weekend.
Laursen, in the last year of his current contract, has made a good recovery from his long-term knee problems and scored against Inter Milan in Saturday's 3-0 win at Villa Park.
He said: "Laursen has a heart the size of a lion and he and Olof Mellberg have played very well together. But that does not mean we don't need some extra players.
"We are looking at that because Martin Laursen, with the best will in the world, could not see a season out. He is just not physically capable of doing that.
"We need people in that position, at full-back and a few others. Gary Cahill is learning his trade and is improving and doing great, but we need someone else in there."