The France international has proved an instant success since joining the Baggies on a season-long loan deal from Marseille on deadline day.
The agreement was made with a view to a permanent transfer and Amalfitano has now hinted that he would be willing to commit to West Brom.
He is in no rush to resolve his future but is feeling happy in England and has been impressed by the performances of Steve Clarke's side.
"The most important thing is to do well here and feel good, which is the case," said Amalfitano in the Express & Star.
"Later on, when the time comes, why not stay? It is a very good collective so it is a good, strong team.
"I have been thinking about the Premier League for a few years and now I am very happy it is happening.
"Now I really want to think about my career and carry on in the best way."
Amalfitano believes he is suited to the Premier League and he has also been encouraged by how his family have settled into their new surroundings.
He said: "I am learning progressively but I felt I needed a change and people have told me that I am a bit English, which is really great.
"It is about my mentality as a player. I am a winner and a hard-worker, which is a bit English.
"I came here with my family and my daughters are going to school. I am here with my wife and they are all settling progressively.
"It is for the best, really, because it's important for my football to be here.
"My wife is pregnant and I've got two daughters, aged six and four. They will probably end up teaching me English at home!"