The experienced Kouyate is expected to be drafted into the Senegal midfield, with the Lions of Teranga needing just a point to secure their qualification from Group H.
Senegal sit second in the table ahead of the final round of matches and know a draw with third-place Colombia in Samara will see them through to the Round of 16 and a possible meeting with England.
Should Senegal lose, however, they will need Poland to defeat Japan by a wider margin to progress.
Hammers new boy Fabianski is tipped to start in goal for the Poles, who have already been eliminated after losing 2-1 to Senegal and 3-0 to Colombia.
With only pride to play for, the goalkeeper will hope to impress and help Adam Nawalka’s side finish a disappointing tournament on a high note.
Should Poland defeat group leaders Japan in Volgograd, then Fabianski’s team could do Kouyate’s Senegal a favour, as the Africans would need just a point to top the table.
If, as expected, the duo are handed starts in Russia, they would become the eleventh and 12th players respectively to start World Cup finals matches as West Ham players.
Bobby Moore was the first back in 1962, before Geoff Hurst and Martin Peters joined him to inspire England to glory four years later.
It would be 20 years before a fourth Hammer started a World Cup match, with Alvin Martin featuring in a vital Round of 16 win over Paraguay at Mexico ’86.
In 2002, Trevor Sinclair was drafted into England’s starting XI on the left side of midfield and played a starring role as Sven Goran Eriksson’s side reached the quarter-finals before being edged out by Brazil.
Joe Cole, who had appeared as a substitute in Japan, became the sixth West Ham player to start a World Cup match in 2006, when he started all five matches as England reached the last eight again.
Onto 2010 and Valon Behrami’s World Cup lasted just 31 minutes before he was sent-off for elbowing Chile’s Arturo Vidal and missed Switzerland’s final two group matches through suspension.
The same finals, in South Africa, also saw Matthew Upson become the third Hammer to score at a World Cup tournament, netting in England’s 4-1 Round of 16 defeat by Germany in Bloemfontein.
Four years later, in 2014, Pablo Armero was still on loan from Udinese when he scored Colombia’s opening goal in the South Americans’ 3-0 group-stage win over Greece in Brazil.
And the same contract situation means Joao Mario was technically still on loan from Inter Milan when he started Portugal’s group-stage games with Morocco and Iran at the current tournament in Russia, and will still be a Hammer when the European champions tackle Uruguay in the Round of 16 on Saturday evening.