The 25-year-old believes the former Porto striker will not be sold, as he feels his side are underdogs against Chelsea ahead of the Uefa Super Cup in August
The Colombia international has been tipped for a new challenge after netting an impressive 36 goals in his debut season at the Vicente Calderon following a €40 million (£31.5m) transfer from Porto last summer.
It has been reported that Atleti are ready to listen to offers for Falcao as they look to balance their books, with Manchester City eyeing a move for either Falcao or Napoli forward, Edinson Cavani.
"I have said before that Falcao would be here with us, and he currently is," Suarez told reporters at a press conference.
"He really likes being at the club, he has said it many times. Atletico's officials have also said that they want him to stay and that he will not leave, so there is no need to talk about this anymore.
"This will be talked about all summer, but we are calm, because that is the type of feeling that he transmits to us.
"He is our goal poacher and we want him to stay."
Atletico's first big challenge of the season comes on August 31, when the side lock horns with Champions League winners Chelsea in the Uefa Super Cup.
"They are the favourites, they are the ones who won the Champions League, but what we want right now is to prepare ourselves, in order to be at the top for that match," Suarez noted.
"This is a goal of ours and it will be a very important match for us.
"We are very excited about it and we know that if we play well, we have our chances to win the game."