The Czech Republic Under-21 international is expected to provide valuable depth to the Spurs squad, particularly after the ankle injury to first-choice goalkeeper Guglielmo Vicario in November - which may still rule him out for the season.
Multiple sources have confirmed that a transfer fee has been agreed upon for Kinsky, although an official announcement from either club is still pending.
The young goalkeeper is expected to undergo a medical and finalise the paperwork this weekend, paving the way for a permanent move to north London.
Kinsky has impressed this season with Slavia Prague, making 29 appearances and recording 14 clean sheets.
Manager Ange Postecoglou has been actively working with technical director Johan Lange to strengthen the squad, especially amidst a significant injury and illness crisis.
Eight players were unavailable for their recent home match against Newcastle United, with the absence of second-choice goalkeeper Fraser Forster forcing Postecoglou to hand 25-year-old academy goalkeeper Brandon Austin his debut.
What can Spurs expect from Kinsky?
Unsurprisingly, the Czech goalkeeper is being touted as the next Petr Cech, the country's legendary Chelsea and Arsenal stopper.
Speaking in October with Rostislav Horáček, the scout who discovered Kinsky as an 18-year-old, Flashscore learnt more about the 21-year-old's playing style between the sticks and his time in Slavia Prague's first XI.
"His style of play is such that he's straight away preventing himself from coming under pressure," Horáček said, describing the keeper's ability with the ball at his feet.
"He plays in such a way that it makes sense and the opponent doesn't immediately go on the break. This makes his job easier for himself, but most of all it helps the whole team.
"He doesn't care which foot he uses to kick the ball. I asked him in training which one he prefers, but he said it doesn't matter. In short, he kicks with both equally.
"In Slavia he has a great defence in front of him. It's difficult for him that he goes 40 minutes without a save and then has to solve a difficult situation quickly. That's exactly what Petr Čech used to do at Chelsea.
"Many times he can do something that would make his job much easier, but he prefers to choose a riskier solution because he wants to solve the situation in a football way at any cost."
Serious contender to replace Vicario?
Vicario's absence has been key to Spurs' indifferent form this season, seeing Fraser Forster concede 20 goals in seven games since suffering a broken ankle in his side's 4-0 win over Manchester City in November.
It's not all Forster's fault though, as a string of injuries to first-choice defensive options like Micky van de Ven and Cristian Romero not helping Ange Postecoglou's cause too much.
Forster has shown moments of quality and made a string of good saves early on, but he's also seen horrific errors punished against the likes of Manchester United and Liverpool.
Vicario had been expected to return in February, but rumours coming out of the club suggest he may not return until next season.
Kinsky would likely go straight into the first XI should he complete his move to Spurs, given his confidence with passing out from the back - something Tottenham regularly do, even to their own detriment at times.
His clean sheet stats will be music to the ears of the manager, too. Spurs have one of the leakiest defences in the Premier League this season, while Kinsky has conceded only seven goals in his 19 league games.