Garde's side have experienced a poor run of two draws and a 4-1 defeat by Bastia in their last three games which have seen PSG put clear daylight between themselves and their challengers.
With nine games left, Carlo Ancelotti's side are favourites for the title but Garde refuses to concede it is a formality.
He told TV programme Canal Football Club: "As long as it's mathematically possible for us to claim top spot come the end of the season, we will continue to believe in our chances.
"For sure, with only two wins in our last seven matches, we're not showing enough but internally - among the squad - I can feel that the players also believe that we can do it."
Lyon face some tough games between now and the end of the season against the likes of St Etienne and Nice before a potentially explosive clash against PSG in their third-last match.
Garde said: "It will be a tough run of matches, but my hopes are high for the end of the season.
"I have a young squad in which there are many youngsters who are just entering the highest level but the pressure simply serves to intensify the competition in the squad.
"But we can't get ahead of ourselves. Our primary objective is give the maximum out on the pitch."
Garde is also hopeful Yoann Gourcuff can make an impact, with injury restricting the midfielder to just eight league appearances this season.
"He's a player who has had more than his fair share of injuries and it has hindered his progress considerably.
"He's a great player but he needs to show more, give more and bring more to the team. And I hope it happens sooner rather than later."