Lasogga is currently on loan at Hamburg from Bundesliga rivals Hertha Berlin and has scored eight goals in eight league appearances.
There is no option for Hamburg to buy the striker during his loan deal and Lasogga has been linked with a move to Atletico at the end of the season.
However, Hamburg's general manager Oliver Kreuzer has discussed the speculation with the 21-year-old and has scotched the rumours.
"I have spoken to him today," Kreuzer told Sky Deutschland. "There is no truth in this transfer rumour.
"Pierre-Michel Lasogga is actually on loan at our club and he is doing a very good job for us."
Meanwhile, Venezuela international Rincon, who is out of contract at the end of the season, has hinted he is now closer to agreeing a deal to stay.
Rincon had previously rejected a new deal, but has held further talks with Hamburg regarding an extension.
"We have spoken about my situation," Rincon told Deutsche Presseagentur. "It has been a detailed conversation.
"We will now have to wait and see what will be offered in the end. Maybe the difference in between is not that much anymore."
Another player who could stay at Hamburg is Jonathan Tah, with Kreuzer holding discussions regarding a first professional contract for the 17-year-old defender.
Kreuzer told BILD: "We are in talks with Jonathan Tah about signing a professional contract.
"We have very much progressed during this round of talks. I feel we will be able to seal the deal in the remaining weeks of this calendar year."