The London Evening Standard reports Kinsky, who was already tied down until 2031, has agreed improved terms with the club to reflect his renewed importance under manager Roberto De Zerbi. Tottenham have also signed Martin Dubravka, 37, as backup, with Guglielmo Vicario expected to leave.
The 23-year-old Czech goalkeeper had a mixed first year in north London. He endured several high-profile errors in the Champions League before turning his form around as the season progressed, and the club's decision to hand him an improved deal signals their belief that he is their long-term first choice between the posts.
Kinsky himself is measured about his position at the club, insisting the competition will be good for him.
"It is a challenge — I will fight for a place during pre-season," Kinsky told Olympijsky Tym. "Negotiations are ongoing with the club about what the future might hold.
"I am interested in staying and fighting for my place because the English league is fantastic."
He was careful not to assume the starting berth is his by right.
"Whether I am the starter or the reserve is something the manager will decide," he said. "In my head I have always been number one, even when I was on the bench. I will have the same approach now, and I believe it will work out."
The contract extension came after a second half of the season in which Kinsky established himself as one of the better goalkeepers in the Premier League, justifying De Zerbi's faith and setting the stage for a genuine competition for the starting position ahead of the new campaign.