The France international is widely expected to depart the Stade de la Mosson at the end of the season and the forward recently admitted that his agent has already held talks with Bayern Munich about a potential move to the Allianz Arena.
However, Giroud, who is under contract to Montpellier until 2013, has now hinted that his future lies elsewhere.
"I do not know yet what I'll do next season, if I leave or stay in Montpellier," he told Telefoot. "But English clubs make me dream, this championship makes me dream.
"But I am not obsessed with England! And money is not a motivation in my career. I make strategic choices of a sporting point of view."
Giroud, who netted for Les Bleus on his full international debut against Germany in February, is Ligue's 1 top scorer this season, having racked up 21 goals in 34 appearances in France's top flight.