Pardew took charge of his first game last weekend as the Baggies secure a 0-0 draw against his former club Crystal Palace.
The new manager was forced to play without several key first-team players, with the likes of Phillips, Brunt, Craig Dawson and Gareth Barry all injured.
Dawson is reportedly making plenty of progress while Barry's thigh injury is not thought to be serious.
Nacer Chadli and James Morrison are hopeful of returning before the end of the year, but Pardew has now revealed Brunt and Phillips could feature against Swansea this weekend.
He told the club's official website: "Hopefully we are going to see Phillips back and hopefully see Brunty back as well.
"It would be nice for Brunty to be back, in terms of being just around the team, because his delivery from set plays is one of the main reasons Albion had a great record at scoring from those.
"I’ve got to say we were disappointing from set plays against Palace and that’s something we can improve immediately."