A number of rumors are currently circulating regarding Triple H and the fact he turned down the executive director role for SmackDown Live prior to it being offered to Eric Bischoff.
The rumors appear not to hold much credibility and one would assume that Hunter has his hands full with NXT right now to take on another big role. Furthermore, Triple H has a lot of creative say and control already so his role as Executive Vice President of Talent, Live Events and Creative would be viewed as senior to both Paul Heyman and Bischoff, although both will report directly to Vince McMahon.
Ryan Satin of ProWrestlingSheet.com shot down the rumor, saying:
"I’ve also heard from multiple sources now who say the rumor of Triple H being offered/turning down one of the Executive Director positions is false."
Sean Ross Sapp of Fightful.com also said much the same:
"I have not heard anything even remotely confirming that Triple H turned down an Executive Director position."