The Colombia international has been heavily linked with a move to Real Madrid this summer but insists he believes in "the project" at Stade Louis II.
The Colombia international was linked with the Santiago Bernabeu side during his time at Atletico Madrid, but he ultimately joined Monaco in the summer of 2013.
Madrid remains keen to lure Falcao back to La Liga, but the 28-year-old insists he is focused on a return to the Champions League with his current club in the 2014-15 campaign.
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"I believe in Monaco's project. I want to stay here and play Champions League football with Monaco," the striker said at a press conference.
Falcao also believes Monaco will strengthen the squad this summer in order to compete with Europe's elite once again.
"We will strengthen the team in order to be ready for the Champions League," he added.
Monaco last featured in the Champions League in 2005-06, when the club was eliminated by Betis in the third qualification round.