The Colombia international returned to club duty on Saturday, after recovering from a knee injury suffered in January that ended his hopes of a FIFA World Cup campaign in Brazil.
However, the powerful forward came on as a substitute against Valencia, in their 2-2 friendly draw at Arsenal's Emirates Stadium.
"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."
Rumours Falcao was set for a departure gained momentum when former team-mate and Real Madrid signing James Rodriguez declared his compatriot was set to follow him to the Bernabeu.
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