Pochettino, however, expects the trio to return for Tuesday's Premier League trip to face Sunderland.
"Toby, Danny and Kane are out. We don't want to take any risks but they'll hopefully be available for Tuesday," the Argentine told reporters on Thursday.
"I think Saturday is not a moment to take a risk and he (Kane) was training in Barcelona (during Tottenham's mid-season training camp) next to the group. But we hope that for Tuesday it is not a problem and he will be available."
Pochettino gave short shrift to reports suggesting Erik Lamela, who has not featured since October, is set to leave Spurs having been spotted at AS Roma.
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The Argentine coach said the winger had travelled to his former club in a bid to accelerate his recovery from a hip injury.
"We will expect that Lamela will be here (on Friday). The last scan in Rome showed there was no issue," he added.
"There are a lot of rumours. He asked to go to Rome to change the place and maybe inspire him to recover quickly, you cannot control all the rumours but he is very happy."
Pochettino said he was planning to visit his former player Ryan Mason in hospital after the Hull City midfielder fractured his skull against Chelsea on Sunday.
"We will go after the press conference to visit him and to see how he is doing. The squad sent a special video message from Barcelona to him," Pochettino said.
"He grew up here at Tottenham -- he is a person that we love."
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by Toby Davis)
