The 25-year-old has scored 12 goals in 15 games in France's top flight.
The Magpies may face competition from Valencia, Villarreal and Malaga, who are also believed to be interested in acquiring Giroud's signature.
Giroud: "I am very happy with the start of the season. I am in good form, in good physical condition so I am lucky at the moment and enjoying my football.
"It is normal to be linked with clubs when you are scoring goals.
"I like the English Premier League. Newcastle are a big club, so who knows?
"But at the moment I am thinking about Montpellier and putting them on the European map at the end of the season."