Nugent is back in training with the south coast club having been on loan at Burnley.
However, his deal with the Clarets does not expire until midnight on Tuesday preventing him from featuring in the vital game against Gianfranco Zola's Hammers.
Goalkeeper David James is reportedly on the brink of joining Stoke but trained with the team on Monday. Mike Williamson is in Newcastle to discuss joining the Magpies and definitely misses out.
Papa Bouba Diop (hamstring), Michael Brown (back) and Steve Finnan (groin) are doubtful too, but Tommy Smith (groin) is back in training and may feature. African Nations Cup stars Aruna Dindane, Nadir Belhadj, Hassan Yebda and Kanu are all absent.
Portsmouth (from): James, Begovic, Mokoena, Kaboul, Mullins, Vanden Borre, Piquionne, Ben-Haim, Brown, Wilson, Hreidarsson, Boateng, Diop, Finnan, Utaka, Webber.