Diego Simeone's long-time assistant Burgos confirmed on Wednesday he would depart his role at the end of the season, having served as his fellow Argentine's number two at Catania and Racing Club before joining him at Atleti in 2011.
Burgos was part of the coaching team that won medals in LaLiga, the Copa del Rey and the Europa League but twice suffered final heartbreak in the Champions League.
In his message to the fans, Burgos spoke about his desire to finally conquer Europe's premier competition and Atleti's superstar goalkeeper Oblak will do all he can to ensure he achieves that feat.
"Without doubt German is a club legend," Oblak told a news conference.
"He is the second hand of Cholo [Simeone]. He does many things that are not seen but he is an important piece of this project and, as he said already, I hope he will leave the club this season as a champion [in the Champions League], that he will make his dream become true."
Oblak is considered as one of the world's best keepers but Lev Yashin remains the only shot-stopper to win the Ballon d'Or back in 1963.
The Slovenia international merely wants to keep performing to the best of his ability so that people keep his name in the conversation.
"Regarding the Ballon d'Or I have thought about that," he added.
"As I always say I am training and playing, I try to improve every day, I am improving, I can improve and journalists and people are who give his opinion, write and talk about me.
"The more people are talking about me the better, I am going to keep working to improve each year and at the end of my career I will be happy.
"I will always give my maximum and at the end we will see what I have achieved."
While that coveted prize has eluded him, Oblak has won the Zamora Trophy – an award presented by Marca to the goalkeeper in LaLiga with the lowest goals-to-game ratio – for the past four seasons.
This season, Oblak faces a battle with Real Madrid goalkeeper Thibaut Courtois – a two-time winner as an Atleti player – but his focus is on team and not individual accomplishments.
"I have never thought too much about this even though it is being mentioned a lot," he said.
"This year is not only Courtois there as well but other two or three goalkeepers doing a spectacular season and that are not conceding many goals.
"But I am not worried about that, only to finish in the Champions League positions, and to end up where we want to be.
"About Zamora, if I finish the season well at a good level, I still can make it, but I never thought much about this."
LaLiga is set to resume later this month after the enforced suspension due to the coronavirus pandemic. Atleti, who are sixth and a point adrift of fourth, visit Athletic Bilbao on June 14.