This has led to sources suggesting the young Czech's form has declined since losing his starting place to Guglielmo Vicario.
The 22-year-old impressed last season under Ange Postecoglou, stepping up during Vicario's long-term ankle injury and delivering several standout performances, including a composed debut display in the first leg of the Carabao Cup semi-final against Liverpool, which Spurs won 1-0.
However, Tottenham were eliminated from the competition after a 4-0 second-leg defeat at Anfield, losing 4-1 on aggregate. Kinsky has struggled to maintain that momentum since the Italian's return to fitness.
BBC Sport's Sami Mokbel has revealed that Kinsky's development appears to have stalled in recent months, prompting unease among the club's coaching staff. "I don't believe a new goalkeeper will be a priority for Tottenham anytime soon," Mokbel said in a Q&A on the BBC Sport website.
"With regards to Kinsky, he made a very promising start to life at Spurs when he arrived in January. But I've been told that his performances dropped off, even in training, once Vicario moved closer to fitness. That certainly raised an alarm for the previous coaching team."
Kinsky, who joined Tottenham in January 2025, has made just one appearance this season, featuring in the Carabao Cup. He remains seen as a goalkeeper for the future, being seven years younger than Vicario, but will need to rediscover his early form to challenge for the No.1 spot again.
Vicario, meanwhile, has faced his own scrutiny this season despite a solid start under new head coach Thomas Frank. The Italian came under fire for his role in conceding against Leeds United, although Spurs still secured a vital 2-1 win that kept them third in the Premier League table.
Frank is not believed to be considering a new goalkeeper in January, but with form and confidence now under the microscope, both Vicario and Kinsky face pivotal weeks ahead as Tottenham aim to maintain their strong league position.
Chelsea have been dealt a major setback after manager Enzo Maresca confirmed that Cole Palmer will be sidelined for another six weeks as he continues his recovery from a groin injury.
Jacob Ramsey is in line to make his long-awaited comeback for Newcastle United after being spotted in full training ahead of Saturday's Premier League trip to Brighton at the American Express Stadium.
West Ham have suffered a major setback after head coach Nuno Espirito Santo confirmed that striker Niclas Fullkrug will be sidelined "for some time" with a thigh injury.
Leeds United manager Daniel Farke has confirmed a new injury setback for Noah Okafor ahead of their crucial Premier League trip to Burnley on Saturday, with several key players still sidelined.
