Frimpong signed on loan from Arsenal on Friday for the remainder of the season. The deal came too late for Frimpong to be involved in Saturday's FA Cup defeat at Manchester United.
However, the 21-year-old is in contention to face the Hammers at Craven Cottage. "He will train with us and then we'll see how fit he is and whether he can play on Wednesday," said Jol.
"I feel he can play a good part in our squad."
Giorgios Karagounis should return to the Fulham starting line-up as they look to stabilise their league position after an extended downturn following their encouraging start to the campaign.
Saturday's meek surrender does not bode well, particularly as United have to be encountered in the Premier League as well next weekend. However, Alex Kacaniklic is confident Fulham can find the improvement they require.
"We know that we need to raise our game and a win against West Ham would put things back on track," he said.
"It's been a difficult period and January has been a strange month for us. It started well with a win at West Bromwich Albion and there was the draw with Wigan, now we have lost our last two games.
"But we are determined to pull through. We want to be a lot higher in the table so we have to start winning again. Hopefully that starts in four days' time.
"West Ham are a good side, but we feel confident of being anyone at Craven Cottage."