A poor run of form for the young Russian following his demotion to the junior team Toro Rosso, coupled with rumors in the Russian media, have led some to conclude that Kvyat's F1 career could be ending at the age of just 22.
But Marko, the head of Red Bull's infamous driver program, told Germany's motorsport-magazin.com: "Kvyat only needs one or two good races to get his self confidence back.
"But he does have confidence," the Austrian clarified. "At the last race at Hockenheim, Toro Rosso was generally poorly unprepared with its new parts."
|Kvyat won't comment on rumors|
(GMM) Daniil Kvyat lashed back at rumors Red Bull is set to dump him completely.
The rumors emerged during the week in the Russian press, indicating that after his demotion to Toro Rosso, his energy drink employer might now be preparing to replace him completely with French youngster Pierre Gasly.
"I'm not wasting any time on damn rumors," the 22-year-old said at Hockenheim.
"Hungary was a bad race so I'm working on having a better one in Hockenheim. I wouldn't take any of these rumors too seriously," Kvyat added.
Along with the Russian rumors is speculation Kvyat is in the running to switch to Williams, where the seats held by Valtteri Bottas and Felipe Massa are both up for grabs.
"Williams would be a good option for him," Vitaly Petrov, who was Russia's first F1 driver, told Sportbox. "It would be a good move for him psychologically as well."
As for the rumors Dr Helmut Marko is set to dump Kvyat, Petrov added: "If this decision really is made, then we will know about it sooner enough.
"It is obvious that there is a certain risk of this, especially as Pierre Gasly from the Red Bull junior program is mentioned in the same information," he said.
07/26/16 (GMM) Red Bull does not intend to renew its contract with Toro Rosso driver Daniil Kvyat for 2017.
That is the claim of the Russian news agency Izvestia, citing the information of a source close to the energy drink company.
Earlier, officials including Dr Helmut Marko and Franz Tost sounded upbeat about the young Russian's future, but the source now gives a different account.
"Red Bull had hoped the return to Toro Rosso would embolden Kvyat, relieving the pressure on him," the source is quoted as saying.
"It was expected that he would score points regularly and become an example for (Carlos) Sainz.
"But in the last seven races, Daniil appeared very uneasy against his teammate, and the most recent setbacks seem to have finally convinced Helmut Marko to not renew the contract."
Izvestia said Frenchman Pierre Gasly seems first in line for the seat, with 22-year-old Kvyat reportedly on Williams' 2017 shortlist.
Red Bull declined to comment.