The Marseille striker is currently sidelined with a thigh injury but is working hard to be fit for Les Bleus' tournament opener against England on June 11
The Marseille striker picked up a thigh injury earlier this month in a Ligue 1 clash with Auxerre, ruling him out of action for up to four weeks.
Nevertheless, Les Bleus boss Laurent Blanc included Remy in his provisional 26-man squad for Euro 2012, despite the forward being in danger of missing the start of the tournament.
"[The recovery] is at an advanced stage where I can resume cycling and spa activities so it's a good omen," Remy was quoted as saying on the French Football Federation's website.
"I am optimistic and confident. Morale is high since I've been fortunate to be part of the [provisional squad of] 26.
"I know if I do not recover in time, it will be problematic. But I'm really confident of being there at the Euros."
Blanc has until May 29 to finalise his 23-man squad for the tournament in Poland and Ukraine, in which his team have been grouped with England, Sweden and co-hosts Ukraine.