The pair – who only arrived at the start of the season – have been linked with moves to Sunderland and LA Galaxy respectively as the transfer deadline moves into view, but Garde has no interest in selling.
Richards has captained Villa this season after moving to the club in June, making 20 appearances in all competitions, while Lescott has featured on 16 occasions.
"There is no chance Micah could go now," the Frenchman said.
"I've got a small squad and then Micah is a player who will play for the rest of the season, there is no chance I will allow players like that to leave. No chance.
"[Lescott] the same, they are players I need for the rest of the season, there is no chance to allow any one of them to leave the club."
Instead Garde is looking to strengthen Villa's squad, but admits completing deals has proved tricky for the Premier League's bottom club.
Garde added: "It took me a few weeks to have an assessment of the team, the squad, the club and then I made some recommendations to the board to try to sign players to improve the team because we need that to be fair.
"The players I recommended I worked on very hard, I tried to sign them, but then for different reasons we couldn't.
"Maybe today there will be late opportunities coming through, you never know, I will still work on that."