The Hammers have completed some very good business this summer already.
Bilic has brought in experienced defender Pablo Zabaleta to solve his problem right back position, England goalkeeper Joe Hart, Marko Arnautovic, striker Javier Hernandez and young prospect Saed Haksabanovic.
But with a net spend of just £10 million so far, there is speculation the Hammers are far from done in the window.
According to the Mail, the 25-year-old - who was a key figure in helping Portugal win the European Championships last summer - has been denied a move to the Premier League before now as Sporting have always proved notoriously difficult to negotiate with.
But West Ham wary are hopeful they can broker a compromise involving Carvalho's new agent Pere Guardiola, brother of Manchester City boss Pep.
They also have Carvalho's international compatriots Jose Fonte and Domingos Quina in East London to help the midfield powerhouse settle in.
Supporters have been reacting in great numbers to the news on Twitter, here's what they've been saying.
Portugal midfielder William Carvalho
Please @davidgold he would be amazing with Kouyate or Obiang in that midfield.— ⚒Jay Bedell⚒ (@JayBedell) August 9, 2017
Been a rumour donkey for Man U and Chelsea for the last few seasons. We have Obiang and Kouyate who are just as good. Need a playmaker.— Riley Cullum (@aceofspies64) August 9, 2017
so sick, please— Liam (@liamions) August 9, 2017
thats too good to be true— michael jones (@apl63) August 9, 2017
I will be gutted if William Carvalho goes to West Ham for £25m. He is a quality DM and Hammers will sell him £50m next summer.— AL48 (@AL48C) August 9, 2017
SIGNING OF THE SUMMER IF WE LAND HIM— Spencer Christian ⚒ (@UnSub_Spencer) August 9, 2017
West Ham Want To Bid For William Carvalho? That's A Statement Real Statement #COYI— Orobokibo (@datsocialdude) August 9, 2017
William carvalho is like a mix of obiang and kouyate, would be good.— Charlie ⚒ (@AyewTakinLePiss) August 9, 2017
Hope I'm proven wrong but absolutely no chance will we get William Carvalho lmao— Ted Powell (@tedwhufc) August 9, 2017
If we sign William Carvalho then I can guarantee that we are going to win the Premier League this year. Won't happen.— Shane Bailey (@ShaneBasuaku) August 9, 2017