The Hammers lodged offers for Chelsea and Sassuolo forwards Armando Broja and Gianluca Scamacca, while one has also been made for Lille midfielder Amadou Onana.
The fees combined are worth £100million as the east Londoners back manager David Moyes.
Last season, the Scotsman struggled at times with no true striker to compete with frontman Michail Antonio.
Their latest actions, though, show the club want to correct that and they are looking for a young and hungry talent.
Broja, 20, showcased his potential on loan at Southampton from Chelsea, scoring six league goals across the campaign.
It's believed the Hammers are willing to pay £25million plus add-ons for the Albanian.
Scamacca, a 23-year-old Italy international, meanwhile, is valued at around £40m by his current club in Serie A.
Onana rounds off the bids with West Ham attempting to land him for £33m plus add-ons.
West Ham have already made three other signings this summer, beginning with been the arrival of Alphonse Areola.
The goalkeeper, who was on loan at the London Stadium last season, joins from Paris Saint-Germain.
Meanwhile, Flynn Downes has arrived from Swansea City and centre-back Nayef Aguerd comes into the squad from Rennes.
If the treble bid is pulled off it could take their spending to almost £150m.