During the summer, Pulis had been keen on signing the Brazilian, only for his attention to be turned to securing the signature of Grzegorz Krychowiak on a loan deal from Paris Saint-Germain.
However, according to the Daily Mail, Pulis is keen to enter the market at the start of 2018 after the Baggies' run of poor form has led to speculation over the 59-year-old's future at The Hawthorns.
West Brom have won just two of their last 20 Premier League games, although the club currently sit in 16th place in the standings despite failing to win in the top flight since August.
Should he remain in the dugout at the West Midlands outfit, Pulis is hoping that 28-year-old Souza can add the quality required to keep West Brom away from the relegation zone.
Since signing from Porto in 2015, Souza has netted 10 goals in 87 appearances for Fenerbahce in all competitions.