Following complaints from a female employee, Horner is under investigation by Red Bull's Austrian energy drinks parent company for his behaviour.
As part of the probe, Horner was recently interviewed by an independent barrister who has been appointed to draw together evidence of the unspecified allegations at the heart of the matter.
Horner has remained in position while the investigation is underway and attended the recent shakedown of Red Bull's new RB20 car at Silverstone as well as the official launch at its Milton Keynes factory.
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But with the new F1 season looming, and there being a risk of the matter casting a cloud over the opening race in Bahrain, grand prix racing's chiefs last weekend urged Red Bull to make it a priority to conclude its investigation as quickly as possible.
"We have noted that Red Bull has instigated an independent investigation into internal allegations at Red Bull Racing," said a statement from F1.
"We hope that the matter will be clarified at the earliest opportunity, after a fair and thorough process and we will not comment further at this time."
With team personnel now travelling to Bahrain, there remains no official word from Red Bull on the progress of the investigation, nor any hint of potential action.
Source: Autosport