British media said ex-England star Gough was on the verge of leaving behind a successful broadcasting career to spearhead Yorkshire's recovery from a damaging racism crisis that has rocked English cricket.
He would replace Martyn Moxon, who left along with the entire Yorkshire coaching staff last week following widespread condemnation of the treatment of former off-spinner Azeem Rafiq.
Rafiq delivered harrowing testimony to British lawmakers last month in which he said his career had been ended by the abuse he received at the English county side.
Long-time Yorkshire player Root, in Brisbane preparing for the opening Ashes Test this week against Australia, said he had not been consulted on Gough.
"I've not heard anything on that, but if that is the case I've obviously spent time with Darren and he's a good man and I'm sure he'll be looking to put his stamp on things at the club," Root said on a zoom call.
"From my experience of spending time with Goughy he is obviously very passionate and knowledgable about the game. His love for it is clear for anyone to see.
"And for the club as well, I'm sure he will be wanting to bring all of that to the fore and all of his experiences and achievements within the game and pass that knowledge onto the group, if it is that he is about to take over."
Root has repeatedly said he cannot recall any instances of racism at Yorkshire, despite Rafiq saying he found his denial "hurtful".
Root on Monday reiterated that he had reached out to new Yorkshire chairman Kamlesh Patel and said that he would pick up the phone if Gough -- who spent 14 years as a player at the club -- called to ask for his help.
"Absolutely," he said. "As I say, I want to do everything I can to help move the club forward. I would welcome any of those phones calls. I've already reached out to Lord Patel and if Gough was to call, absolutely."
Last month, the England and Wales Cricket Board unveiled a 12-point action plan to combat discrimination in the sport, including a review of dressing-room culture.
