The pair have remained in Auckland following Wednesday's 2-1 pre-season loss to A-League side Wellington Phoenix.
Manager Sam Allardyce remains relaxed about the result but was a bit more critical of the Phoenix's physical play following Louis Fenton's tackle on Kouyate.
Although the midfielder played on after the heavy challenge, he left Eden Park on crutches.
"(The injury) is just above the ankle where the boy tackled him," Allardyce said. "He was rather fortunate he didn't break his leg. We're pleased about that.
"Cheik has gone for a scan to make sure there is no more damage than we've assessed so far.
"He was limping this morning but not as bad as he was last night, which is a good sign. The scan is a precautionary measure.
"Tomkins got a groin strain towards the end of the match. There was little point in us flying them all the way here, so they're getting attention from our physio back in Auckland."
West Ham will play Sydney at Westpac Stadium in the first match of a double-header on Saturday that will also see the Phoenix take on Newcastle United, who defeated Sydney 4-0 in Dunedin on Tuesday.
Allardyce will be keen to see his side build on their second-half performance in Auckland when they take on Sydney, especially when it comes to converting chances into goals.
"That was a little bit of a concern, the amount of chances we created in the game and didn't convert any more than the one goal," he said.
"But in terms of the tempo of the game I thought the lads got a really good workout so it did really lift the match fitness levels to another level."
Building match fitness and giving more of the squad game time will shape Allardyce's selection for Saturday's game and he refused to be drawn on whether Mauro Zarate, who came off the bench to score against the Phoenix, will start.
"He might do," was the manager's cagey response. "We gave some players more time than others and we've got to equal that for the players that have come all this way and haven't had that much time on the field yet."
