Manager Ange Postecoglou is currently dealing with a squad crisis which has seriously impacted his options in goal.
First-choice goalkeeper Guglielmo Vicario remains out with a long-term ankle injury, while back-up Fraser Forster has been struck down with illness ahead of the Premier League visit of Newcastle on Saturday.
As first reported by talkSPORT, it means Spurs will hand 25-year-old Brandon Austin his senior debut for the lunchtime clash - nine years after the goalkeeper arrived at the club in 2015.
Tottenham have acted quickly to address the issue by landing Czech Republic youth international Kinsky in the January market.
The 21-year-old is flying to England for a medical on Saturday evening.
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Kinsky has impressed in the Czech top-flight this season - keeping 12 clean sheets in 19 games and helping Slavia Prague top the league.
He unexpectedly broke into the first-team after No.1 goalkeeper Jindrich Stanek suffered a serious injury before the 2024/25 season.
Questions have been asked of Forster during Vicario's absence, with Tottenham conceding 15 goals in their last seven outings.
Speaking about the need for reinforcements in January, Postecoglou said on Friday: "It's not a matter of pushing but I think the club are working hard to try and sort of get some help for the playing group and it's no secret, we need to bolster our numbers up a little bit. January is not an easy month.
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"We understand it's not an easy time to bring people in particularly quickly. At the same time we still want to make sure we do what we think is the best thing for us rather than sort of just, you know, panic and bring people in who aren't going to be a suitable fit.
"They are not having New Year parties, they are out there working trying to improve our situation and they'll continue to do so."
In total, Tottenham are currently without eight first-team players due to injury, suspension and a sickness bug in the camp.
Beyond their goalkeepers, Spurs have been significantly affected in defence, with first-choice stars Destiny Udogie, Micky van de Ven and Cristian Romero all sidelined.
Postecoglou's men have struggled throughout the squad crisis, winning just once in their last seven league matches and plummeting to 11th in the Premier League table.
When asked if the situation has lift him pulling his hair out, Postecoglou responded: "I'd be no good bald, my wife would definitely leave me!
"I've never been this kind guy who is 'woe is me' and 'can anything else go wrong'. It's a hell of a challenge.
"I keep telling the guys in there that it's just going to make the story better and more interesting at the end, wherever we end up."
talkSPORT understands Tottenham are also considering a January swoop for AC Milan defender Fikayo Tomori.
Newcastle, West Ham and Brentford are also keen on the former Chelsea centre-back amid his recent struggles in Italy.