Payten, a prop who won a title with the Wests Tigers, was an assistant to Green when the Cowboys won their inaugural title in 2015.
The Telegraph reported Payten was known for his "straightforward style".
"The Warriors may now jump early to sign Payten to ward off North Queensland's interest," it claimed.
Speculation is rife in the NRL over coaching appointments and there were no sources identified in the Payten-Cowboys story.
The Warriors have identified a long list of candidates, with the decision to be made by owner Mark Robinson, chairman Rob Croot, CEO Cameron George and club legend Simon Mannering.
The club has always made it clear to Payten that they were heading to the open market in search of a coach, although Payten was on the formal interview list as well.
Green has also been linked with the Broncos, who are in a horror patch under Anthony Seibold who is being described as a "dead man walking".
Green, who will get a $1m Cowboys payout, said: "I'm going to have a nice break and look after my family.
"Obviously I want to keep coaching and it looks like there's lots of jobs going."