The striker has spent the last eight months on the treatment table with a serious knee injury but at last made his comeback on Saturday
The Colombia international damaged the anterior cruciate ligament in his left knee during Monaco's Coupe de France victory over Monts d'Or Azergues in January.
Falcao missed the remainder of the domestic season, as well as his country's World Cup campaign in Brazil, which ended in quarter-final defeat to the hosts.
But on Saturday, the 28-year-old made his comeback as the Ligue 1 runners-up drew 2-2 with their Spanish opponents in the pre-season tournament's curtain-raiser at Arsenal's Emirates Stadium.
And Monaco boss Leonardo Jardim is hoping the striker will be able to play 60 minutes on Sunday as his side face the Gunners in their second game.
He said: "Falcao played for 20 minutes to help him overcome his anxiety, which is natural when you come back after six months without playing.
"He played well. It was important for him to play a bit, so tomorrow he can play from the beginning. Let's see tomorrow if he can play for 60 minutes or just 45."
Falcao entered the action in the 72nd minute, coming off the bench to replace Dimitar Berbatov.
Monaco were 2-1 down at that stage, having taken the lead through Ruben Vezo's own goal on the half-hour mark.
Another own goal levelled the scores, Ricardo Carvalho putting through his own net, before Paco Alcacer put Valencia in front for the first time after 69 minutes.
Jardim introduced Falcao shortly afterwards, and Lucas Ocampos' strike 10 minutes from time ensured Monaco avoided defeat.