Dubravka left Burnley this month following their relegation from the Premier League, bringing to an end a stay at Turf Moor during which he made 35 appearances but could not prevent the club finishing in the bottom three.
The veteran made 179 Premier League appearances for Newcastle United across eight years before a brief loan spell at Manchester United in 2022-23, and arrives at Spurs with substantial top-flight pedigree.
His signing would coincide with the expected departure of first-choice goalkeeper Guglielmo Vicario, who is widely anticipated to return to Italy — most likely to Juventus — this summer.
Kinsky, 23, who stepped in for Vicario during the run-in and played a key role in keeping Spurs in the Premier League, is set to become the club's new number one. Tottenham are also considering a contract extension for the Czech international, whose future had looked uncertain after being substituted after just 16 minutes of a Champions League tie at Atlético Madrid under caretaker Igor Tudor.
Elsewhere, Spurs are pursuing Newcastle United midfielder Sandro Tonali, having had an initial offer of £75m turned down last week. The club are expected to return with an improved bid, and Tonali is understood to be open to the move, though a switch to Premier League champions Arsenal may be his first preference.
Tottenham have already added Brighton defender Jan Paul van Hecke for £52m and are also monitoring West Ham's Mateus Fernandes, though Manchester United remain the frontrunners for the Portugal midfielder's signature.