French daily L'Equipe claims that both Newcastle United and Aston Villa have expressed an interest in the 47-year-old.
Galtier is highly rated on the other side of the Channel, and has taken St Etienne close to UEFA Champions League qualification in France although they look set to just miss out to Lille on third place.
But with two games still remaining in Ligue 1, Galtier - who has been in charge of St Etienne since 2009 - would not talk about the reported interest in him.
"My duty and my dedication means that I have to prepare for next season," he said.
"But we are never sure of anything in football. It is very difficult to talk about the future of a coach."