Lloris is in his 10th season at Spurs but he is expected to leave when his contract expires in 2024 and the club are making plans for life after the 35-year-old France World Cup winner.
Tottenham have identified Oblak as a primary target to be their next No1 and have sounded out the Slovenian about a possible move for him next summer.
Spurs head coach Antonio Conte has spoken to managing director Fabio Paratici about a long-term plan to eventually replace Lloris.
The France captain, who has made 425 appearances for Spurs, signed a two-year contract in January and is still one of the most consistent keepers in the Premier League. But he is in the back end of his career.
Oblak has a contract with Atletico until 2028 but the Spanish club are prepared to discuss a transfer for the 29-year-old after almost a decade of service.
Tottenham could face competition for Oblak from Manchester United, who have asked to be kept informed about his situation amid doubts over the future of David de Gea.
Oblak joined Atletico in 2014 and established himself as one of the finest goalkeepers in Europe. He helped Atletico reach the Champions League Final in 2016 and played a key role in their La Liga title triumph in 2021.
Oblak has in the past declared his interest in moving to the Premier League. A £107m release clause had stopped English clubs moving for Oblak but that figure is thought to have lowered significantly. His new contract put him in the top five best-paid players in Spain.
Chelsea had made contact with Oblak through their former technical advisor, Petr Cech, when Frank Lampard was in charge, but there has been no indication from their new owners that they will revisit their interest.
That is despite new co-owner Todd Boehly drawing up a shortlist of possible goalkeeper targets. Edouard Mendy is unhappy with the terms of the new contract he has been offered and doubts remain over the future of Kepa Arrizabalaga.
Tottenham signed Fraser Forster on a free transfer last summer to act as back-up to Lloris but he is not viewed as a long-term successor.