Under the terms of the deal that took him to The Hawthorns from his parent club Marseille, the 29-year-old is due to return to his French employers during the summer.
However, his representative Willie McKay has insisted that while the Baggies may have missed their chance to sign Amalfitano on a permanent basis, the one-time French international is keen to stay in the Premier League.
"West Brom would like to sign him, but they have missed the cut off point in the loan deal to make it permanent as they were unable to commit to a deal due to the uncertainty over their Premier League status," McKay told Sky Sports News.
"I know a lot of other Premier League clubs are interested in Morgan and are monitoring developments. Morgan has really enjoyed this season at West Brom and he would love to stay in the Premier League."
Amalfitano has scored four goals during his 28 outings this season.