Christian Horner may reportedly find out the result of his investigation later this week with F1 bosses calling for the situation to be "clarified at the earliest opportunity".
Horner met with investigators earlier this month at a secret location in London as he was probed over allegations made by a female employee at Red Bull.
The 50-year-old, who denies the allegations was then present at Red Bull's car launch on February 15.
But there has been no resolution to the investigation as of yet with pre-season testing getting underway this week.
Christian Horner may find out the result of the investigation soon
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Red Bull are reportedly desperate for the matter to be resolved before the season-opener on March 2.
According to the PA, a conclusion could be reached by the end of the week.
It comes after F1 made its first official comment on the investigation into Horner on Sunday.
"We have noted Red Bull has instigated an independent investigation into internal allegations at Red Bull Racing," the statement said.
"We hope matter will be clarified at the earliest opportunity, after a fair and thorough process. Will not comment further at this time.
"The FIA have since followed suit, adding they won't be making any comment until the investigation is finalised.
"In relation to the independent investigation currently being undertaken by Red Bull GMbH, the FIA reiterates that until such time as the investigation has concluded and the outcome is known, we will not be commenting further," their statement read.
"The FIA remains committed to upholding the highest standards of integrity, fairness and inclusivity within the sport."
Horner has reiterated his innocence ever since the allegations were first made against him and cut a defiant figure at the launch of Red Bull's RB20 last week.
When asked whether there was any doubts on his own position at the helm of Red Bull, Horner said: “No, not at all. Absolutely not.
Christian Horner has denied the allegations against him
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"I’m fully committed to this team, I’ve built this team, I’ve convinced people to come here and work here.
"I enjoy working with the team, with the people. The biggest asset of the team is the people and that continues to be the case.
“Look I’m absolutely committed to this team.
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Christian Horner spoke for the first time at Red Bull's car launch
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“I’ve been here since the beginning, I built this team, there’s been highs and lows along the way as you’ve seen in some of the videos that you’ve seen earlier.
“We’ve won 113 races, we’ve won seven drivers’ world championships, we’ve won six constructors’ world championships in 19 seasons, and that’s in the history books now but it’s what lies ahead that’s always important.
“And so my focus is on the future, is on Red Bull Powertrains becoming… operating a start-up engine business.
"We have an advanced technology business that is going to be producing the first Red Bull track car and of course there’s an awful lot going on on the campus and investment on the campus as you can see.”