The Bluebirds captain has agreed terms on a move which could be worth up to £5 million, depending on add-on fees.
Trollope hopes to use those funds to sign a striker before the transfer window shuts on Wednesday.
"Time will tell the scope for reinvesting," Trollope explained.
"He's been a fantastic servant and we wish him well. The Premier League's come calling, he's a great fella and he was captain, so we're going to miss him.
"But people have their price and Hull got to that, and the club were willing to accept it."
Marshall was left out of Cardiff's squad for Saturday's 1-0 defeat by Reading, a misfiring display which exposed the Bluebirds' attacking weaknesses.
Trollope's side created a handful of chances but they were squandered by the likes of makeshift forward Lex Immers.
Just as with strike partner Anthony Pilkington, Immers is a midfielder who has been playing in a more advanced role as Cardiff struggle to find a genuine centre-forward.
They signed Frederic Gounongbe and turned Kenneth Zohore's loan into a permanent transfer during the summer, but both strikers have looked out of their depth in the Championship.
Trollope sees potential in Zohore - who at 22 is six years younger than Gounongbe - but the former Wales coach wants to bolster his attacking options before Wednesday night's 23:00 deadline.
"We're looking to strengthen in the attacking department. We need a striker," he said.
"We've been looking hard. We've got a set of strikers here, some are not natural strikers, some have done well in the position.
"We've got Gounongbe who's still adjusting to the British game, I think that's fair to say. He's had chances in all the games and not quite taken them.
"Lex and Pilks [Pilkington] provide different options and Kenneth Zohore is a young man with a big future ahead of him, but he needs guidance and improvement.
"So we are looking for one. We're hoping to do business before Wednesday because we do need one."
Cardiff City boss Paul Trollope will have to wait to discover if he is able to spend the money generated by the impending sale of goalkeeper David Marshall to Hull City.