The Baggies are looking for a new manager after opting to sack Steve Bruce and they have been linked with wanting Rowett.
It has been suggested that West Brom want to hold talks with Rowett as they look to take him to the Hawthorns.
However, West Brom have not yet made contact with Millwall to ask for permission to hold talks with Rowett.
The former Birmingham City boss has been in charge at Millwall since 2019 and led the club to a ninth place finish in the Championship last season.
Millwall are likely not to be keen on losing Rowett, but it remains to be seen if he is tempted by the West Brom post.
The Baggies are currently inside the relegation zone in the Championship after winning just one of their 13 league matches so far.
Millwall are due to play host to West Brom in the Championship later this month.
