Swansea have a defensive crisis with Garry Monk, Izzy Iriekpen and Kristian O'Leary ruled out of Saturday's match.
29-year-old ex-Nottingham Forest man Edwards will join on an initial one-month deal, but Swansea say both parties are keen for the move to became a permanent one.
"It's an opportunity for us to look at a player who did well for Swansea first time round," said boss Kenny Jackett.
Edwards began his League career at Swansea, making 112 League appearances before joining Forest for £275,000 in 1998.
He has won one Welsh international cap.