Coleman’s future with the national side is currently up in the air after he failed to guide the Wales to the 2018 World Cup following their 1-0 loss to the Republic of Ireland earlier this week.
The 47-year-old had previously said that he would step down from his role after the World Cup but he is yet to make an official statement.
Reports have linked a number of candidates with the role and Baggies boss Pulis is understood to be one of the contenders to take over.
However, Pulis has moved to shoot down hose claims and insists he has no interest in leaving his current post at the Hawthorns.
Pulis said: “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.
“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.”
Preston are reportedly weighing up whether or not to make a fourth offer for Peterborough United left-back Andrew Hughes.
James Maddison has completed his move from Norwich City to Leicester City for an undisclosed fee.