Horner is exploring a way back to the paddock after he was sacked by Red Bull last year.
The third major of the year starts on June 18 at Shinnecock Hills.
Steve Borthwick revealed in May he was considering resting his captain for all, or part, of the Nations Championship in July.
The ECB, the Cricket Regulator and Saracens are investigating events which took place in the early hours of Monday morning at a London nightspot.