Verstappen unfazed by Horner speculation before F1 season opener
Horner's future with the outfit was thrown into doubt after he was accused of alleged controlling and improper behaviour by a female Red Bull team member, a claim that initiated an independent investigation.
"It doesn't affect me," Verstappen said before this weekend's season-opening Formula One Grand Prix in Bahrain.
"I'm very focused on the car and on myself and, hopefully, it is resolved very soon," he added.
Horner denied all the claims and continued to work as usual in the build-up to the new season while the probe was completed.
It has been reported that the outcome is due to be made public on Thursday.
The 26-year-old Dutchman kept his responses brief to questions from reporters at the Bahrain International Circuit where he won last year's race for the first time.
"It's a whole team effort and everyone sticks together," he said.
"And we all work for success and that's why it should be resolved very soon."
Seven-time champion Lewis Hamilton of Mercedes, the most successful driver at Sakhir with five wins, said the investigation into Horner's behaviour was 'hanging over the sport' and that the outcome was important for the future.
"It's a difficult one to answer," said Hamilton, who announced earlier this month he will leave Mercedes and race for Ferrari in 2025.
"I think we always have to do more to try and make the sport, and the environment that people work in, feel safe and inclusive.
"Any allegation has to be taken very seriously.
"Obviously, we don't know everything that's going on, but it does need to be resolved as it is hanging over the sport."
'Role models'
Hamilton added it would be "interesting" to see how the Horner case could change Formula One in future.
"It's a very important moment for the sport to make sure that we stand true to our values."
His words echoed those of Mercedes team chief Toto Wolff.
"We are a global sport and one of the most important sport platforms in the world and we are role models," Wolff said.
The investigation was conducted by a British lawyer whose dossier was due to be submitted to the Red Bull parent company in Austria on Tuesday.
Verstappen was unruffled by the discussion about Horner and remained calm and focussed on his job.
"I feel very comfortable in the car," he said of the RB20, a car which marks the team's 20th birthday at a circuit this weekend which itself celebrates two decades on the Formula One calendar.
"But only time will tell how we do and if we are successful.
"We had some good testing days and I felt good in the car. It looks promising, but you never really know in advance where you stand."
Horner, who is married to former Spice Girl pop singer Geri Halliwell, was not expected to attend Wednesday's media day in Bahrain, but to be at the circuit on Thursday for opening practice.
The race takes place late on Saturday under floodlights instead of Sunday to accommodate Ramadan, which starts on March 10, in the early-season schedule.