The 21 year old appeared as a substitute in Southampton's opening match of the Championship campaign, as they beat Wrexham 2-1.
He was the club's Player of the Year last season, making 36 Premier League appearances following a £15million transfer from Sporting CP.
The Guardian report that West Ham are now preparing their opening bid for Fernandes, who is the number one target for boss Graham Potter.
They add that the Hammers assessed options including Aston Villa’s Jacob Ramsey and Lille’s Ngal’ayel Mukau, but have listed Fernandes at the top.
West Ham are said to have followed Fernandes for over a year and were interested last summer, before deciding to pursue other options.
The report adds that £30million could see a deal between the two clubs happen, but we understand Saints value Fernandes significantly higher.
Saints manager Will Still has already confirmed there is a lot of interest in the Portuguese youth international, following his first season in England.
Still told us: "I hope [he stays]. I know he's a good player. I know there's interest. That's normal when you've got quality players like him.
"I think the club has been clear. If he leaves, he'll leave at the right price and we'll be able to replace him. I'm not too worried about that.
"We know that as long as he's here, we can use him and he'll be good. And if he goes, then I'm sure everyone will come out bigger and better from it."