But the prospect of Horner's fate being decided before the Formula One world champions unveil their 2024 car next week appears unlikely.
Reports in Britain's Press Association and the BBC suggest there was still no resolution to the affair after the 50-year-old Briton, who has been team principal since 2005, was interviewed for eight hours.
There was no comment from Red Bull Racing, nor parent company Red Bull GmBH, which launched the investigation following an accusation from a female employee - a claim Horner has categorically denied.
The BBC suggested it could take weeks for the matter to be resolved.
Red Bull are going ahead with their car launch next Thursday, which will undoubtedly now be hijacked by the inquiry.
Pre-season testing is then scheduled for Bahrain on February 21-23 with the 2024 season opening in the Gulf State on March 3.
Dutch newspaper De Telegraaf broke news of the allegation at the start of the week involving the man at the head of the team which last year carried Max Verstappen to his third consecutive world title.
Red Bull GmBH the Austrian energy drinks company that owns the team, confirmed on Monday that an independent investigation had been launched.
Asked about the accusations, Horner told De Telegraaf: "I completely deny these claims."
Horner, who is married to former Spice Girl Geri Halliwell, has been in charge at Red Bull since they entered Formula One 19 years ago.
During that time he has overseen seven drivers' world championships and six constructors' titles.
The team dominated last season, winning 21 of the 22 races in 2023 as Verstappen defended his drivers' crown.