It is understood that Garde is one of at least three people Newcastle have spoken to and the club will be speaking to one more candidate within the next 24 hours.
John Carver has been put in temporary charge of the first team following the departure of Pardew to Crystal Palace and he oversaw a 2-0 defeat to Chelsea at Stamford Bridge on Saturday.
Garde has Premier League experience as a player having joined Arsenal on the same day as Patrick Vieira in 1996 and he made 10 appearances in the double-winning side of 1997/98.
The 48-year-old was in charge of French side Lyon for three seasons after succeeding Claude Puel in 2011 before departing last summer for personal reasons.
One manager who has taken himself out of the running for the Newcastle job, however, is Ajax coach Frank de Boer.
De Boer, who has won four Dutch league titles in a row, said: "I feel flattered that my name is continuously linked with Newcastle. But it is not a club I have ambitions for now.
"They are a sleeping giant and I love their fans. They also have fantastic facilities. But I don’t want to think about joining them. I prefer to put my energy into other things."