Fletcher, who has worked under the likes of Sir Alex Ferguson, believes Pulis is constantly overlooked for top jobs but he could easily make the transition and manage a big club.
West Brom take on Arsenal this weekend and the Gunners could be looking for a new man at the helm in the summer with constant speculation about Arsene Wenger's future and Fletcher believes Pulis could handle such a post.
He said: "There is no doubt he could handle the top four. There is no doubt about it. He is focused, driven. This is the way he works. You are under no illusions what is expected of you. Personalities like that can handle big personalities.
"He has got the experience. If he got offered a top-four job tomorrow he would treat it like he has every other job. He would walk in and be himself, be comfortable in himself."