West Brom failed with an approach to sign Brazilian in the summer.
A defensive-minded midfielder who is also capable of filling in at right-back if required, De Souza is vastly experienced and has previously been capped by Brazil.
West Brom are eager to strengthen their squad following a miserable start to the season that has left them in 16th place in the Premier League.
Manager Tony Pulis is under intense pressure, especially with West Brom facing a challenging upcoming schedule which includes games against Chelsea and Tottenham Hotspur.
Although West Brom brought in Grzegorz Krychowiak on loan from Paris Saint-Germain in the summer they still lack steel in midfield and the acquisition of 28-year-old De Souza, who is capable of making precisely-timed challenges with regularity, would certainly help to address that issue.
Given that they have mustered just nine goals in the Premier League so far this season, a new striker should surely also be under consideration for West Brom.