Antonio Conte, the Spurs head coach, is hopeful of having Bentancur back for the north London derby against Arsenal on January 15.
Kulusevski missed the 2-0 defeat to Aston Villa on New Year Day's with a muscle injury and Conte suggested he would leave the decision on whether he will feature at Selhurst Park to the player.
Bentancur returned from the World Cup with an adductor injury, while Richarlison is set for a further MRI scan on a hamstring injury picked up in Qatar.
“Rodrigo Bentancur has started to work, he is not still ready for this game and also for the game in the FA Cup [against Portsmouth on Saturday] but we hope to have him for next game in the Premier League [against Arsenal],” Conte said.
“About Richarlison, we have to see. We have to check the situation and for sure in the future he will have another MRI to understand very well which is his situation.
“About Kulusevski, it is not a serious injury but we have to monitor it day by day, today and tomorrow, and we have to take the best decision.
“I don’t know [if he will play against Palace], honestly. Now, I don’t know because we have today and tomorrow to check his situation.
“For sure, we will see. If the player gives his availability, he could play. Otherwise we have to wait and to have patience for the next game.”
If Kulusevski is not fit, Bryan Gil is expected to keep his place on the left of the front three but Conte admitted his side are “in trouble” without Richarlison and the Swede.
“If you have four players, the strikers who are usually the creative players, and two are injured, we are in trouble,” Conte said. “Because we have two players [left] and then we have Gil, who is a good player who understands football very well but he is a young player and you have to try to give him time, to wait and then have a ready player.
“Now Gil is playing. The last game, honestly he satisfied my expectation and probably he's going to play tomorrow, I don't know but it's possible. Without two players, especially up front, we are in trouble."
Conte will also be without the suspended Yves Bissouma, so Oliver Skipp or Pape Matar Sarr will start alongside Pierre-Emile Hojbjerg in the midfield.
“This is another opportunity to see a young player, Skipp or Sarr tomorrow," the Spurs head coach said.
“For me it's important to understand the improvement they're going to do. This is the road we're following. This is normal. I repeat, tomorrow we'll see another young player and we'll make an evaluation then.
“Skipp in my opinion last season played two or three months very well before he had an injury. But we're talking about a player who is 21, 22. Like Gil, like Sarr, like [Ryan] Sessegnon, [Djed] Spence and all the Under-21s."