The Dragons failed to qualify for the 2018 World Cup, even missing out on a playoff spot courtesy of a 1-0 home defeat against Republic of Ireland on Monday night.
Coleman is currently considering his position in charge of the national team, but Newport-born Pulis has rejected the speculation linking him with the position should it become vacant.
"I'm quite happy where I am and I think it's wrong we're even talking about someone who's still in a job," he told reporters. "Chris has done a fantastic job there and he'll be very disappointed at the moment, as the nation are.
"Time is a great healer, we'll see what Chris does in the next couple of months."
Pulis, who has been at The Hawthorns helm since January 2015, takes his side to Leicester City for their next outing on Monday night.