Sporting Lisbon manager Ruben Amorim flew to the UK on Monday for face-to-face talks with West Ham.
Amorim has emerged as a surprise contender to replace David Moyes alongside ex-Wolves manager Julen Lopetegui.
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The 39-year-old has been heavily linked with Liverpool but at this stage he is not one of the frontrunners to succeed Jurgen Klopp.
West Ham look certain to appoint a new manager at the end of the season.
Moyes is out of contract this summer and while West Ham insist no final decision on his future has been made, it is now increasingly likely he will leave at the end of the season.
Moyes has been in charge of West Ham for four-and-a-half years and guided the Hammers to their first major trophy since 1980 with Europa Conference League glory last season.
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But a large section of fans have expressed frustration with the club's style of play under the Scot, with Sunday's 5-2 thrashing at Crystal Palace increasing calls for Moyes to go.
talkSPORT understands former Wolves boss Lopetegui has also been put forward as a potential replacement for Moyes, while Thomas Tuchel is another name being linked to the role.
Now Amorim is firmly in the frame and held talks with West Ham chiefs in London on Monday.
The Portuguese has made waves in his homeland having won the Taca de Liga, the Portuguese League Cup in his first managerial gig with Braga.
He then got the Sporting job in March 2020, winning the Primeira Liga in his first full season at the club where they beat Benfica and Porto to the title.
Amorim has also scooped two further Taca de Liga titles while at Sporting, and the club are on course to win another league title this season as they sit seven points clear at the top.
Gabby Agbonlahor reveals he did his coaching badges with Liverpool managerial target and Sporting CP head coach Ruben Amorim
talkSPORT's Gabby Agbonlahor did his coaching badges with Amorim and the ex-Aston Villa star is convinced that whichever team that gets him in the summer will be fortunate.
"Funnily enough, I did my coaching badges with Ruben, we did the fast track, Northern Ireland, Belfast course," Agbonlahor told talkSPORT earlier this month.
"He was on it. Some people might have had a little laugh and joke on the course and stuff, he was on it.
"Concentrating in every meeting, all the theory part, when you did the coaching stuff on the pitch you could tell that he was on it.
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"That was five years ago, he's 39 now so he's quite a young manager but I don't see why not [he could become Liverpool manager], he's doing a great job at Sporting, isn't he?"