Albion may have to shatter their transfer record again to land another striker.
More firepower is the top priority before the transfer window shuts at the end of the month following the arrival of central midfielder Davy Propper from PSV Eindhoven for around £10 million.
Chairman Tony Bloom told The Argus: "It's pretty obvious we are looking to bring in another centre-forward. It's a difficult position to fill, that's not just froth, but they are highly sought after and we look forward to the next few weeks and getting the right one in before the end of August."
Albion have now added Propper, keeper Mathew Ryan, left-back Markus Suttner, No.10 Pascal Gross and on-loan attacking midfielder Izzy Brown from Chelsea to the squad that won promotion.
They also want to add a right-back and third-choice goalkeeper before the August 31 deadline, but Bloom has been stunned by the spiralling scale of transfer fees.
He will do his upmost to give manager Chris Hughton the best possible chance of keeping the Seagulls in the Premier League, without plunging the club into difficulties if they go back down.
Bloom said: "The players we have recruited so far we are very happy with and we have more work to be done. But we don't want to be spending a huge amount of money and there is no guarantee that it will be successful.
"If you do go back down you are back in a situation of a lot of clubs who are really struggling after relegation.
"It is always getting that balance. You are trying to get value for money for every player you bring in, which in this particular window is not easy as the inflation on the transfer fees is quite sensational.
"I might not like paying them but I have to get the best value out there, with also the knowledge that sometimes you have to individually overpay if you need a particular type of player, because we want to give ourselves within our budget the best possible chance of staying in the division.
"So it is balancing these things up. There is no doubt it is an inflated market, but who is to say that it is not going to keep inflating in years to come?
"It has never stopped. I expected it to be some kind of inflation this season, but I was not quite expecting this level and I think I am probably in the majority with that view.
"I am surprised. I don't get surprised by too much, but how much it is, how much clubs ask, I think it's even a bit more when more when you are in the Premier League.
"But we get on with it. It's the same for everyone. Our competitors in other Premier League teams are finding it very difficult. All I can say is that we are extremely pleased with all the players that we have brought in.
"You are rarely going to get all the transfers you want before the first game of the season, but we have got a lot in and we are looking forward to the next few weeks and completing our squad."
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