Arsene Wenger is thought to be a big fan of Grenier, who has just one year left on his Lyon contract. The Frenchman, who was called up to the France squad for their upcoming friendlies, has held talks with the Ligue 1 giants over a possible extension.
And Garde believes Griener, along with midfield teammate Maxime Gonalons, would be best served by staying put.
Speaking to French newspaper L'Equipe, Garde said: "There are stories about some players leaving the club. The last few years we have won the Coupe de France and finished third in the league.
"Am I keen to accept the transfer of Gonalons and Grenier? No, because they are exactly in our project and I want to build the team around them. If Grenier achieved such a level it is because he has worked so hard.
"We have been much more demanding with him like all our young players. But he convinced everyone, he did everything to be at the core of our project in the coming years."
Grenier, a 22-year-old playmaker, came through the Lyon academy before making his first-team bow in 2009. And he's become a key part of the French side's midfield, along with Gonalons.
Grenier is yet to make his France debut, while Gonalons has six caps for the national team and predominately plays in a withdrawn defensive midfield role.
Garde added that he hopes Yoann Gourcuff will also stay at Lyon despite speculation linking him with a move away from the club.
One France youth international who looks set to move to Arsenal is Yaya Sanogo. The French under-21 striker is close to agreeing a permanent move to the Emirates Stadium.