The striker has been heavily linked with a move to Real Madrid but his coach is determined not to see him follow James Rodriguez to the European champions this summer
The Colombia international returned to club duty on Saturday after recovering from a knee injury suffered in January that ended his hopes of a World Cup campaign in Brazil.
The powerful forward came on as a substitute against Valencia in their 2-2 friendly draw at Arsenal's Emirates Stadium, shortly before Real Madrid - who have been heavily linked with a summer swoop for the player - suffered a 3-1 defeat to Manchester United in America.
Jardim has already seen James Rodriguez move to the European champions and is determined not to lose Falcao before the start of the season.
"At this point Falcao is our player and he's with us 100 per cent and we don't want to let him go," Jardim said.
"It's a pity we lost James [Rodriguez] but we can count on Falcao staying. Regardless of what people say, he's our player.
"He's in the final stages of his recovery and he'll be with us this season."
James has already admitted he would relish the chance to link up once again with Falcao at Santiago Bernabeu.