The French club will not sell the Colombian striker at any price, but are interested in signing goalkeeper Diego Lopez.
Radamel Falcao will not be joining Real Madrid this summer, according to Monaco coach Leonardo Jardim.
The Colombian striker netted the winner against Arsenal in the Emirates Cup, and after the match Jardim stressed that Monaco had no intention to sell, describing Falcao as "untransferable" and "indispensable".
"At this moment in time, Falcao is our player, and he is with us 100%," he told Ligue1.com. "We don't want to let him leave.
"It's a shame that we have lost James Rodriguez, but we can count on Falcao. It matters little what people say, he's our player. He's in the last stage of his recovery, and he'll be with us this season."
Monaco have already sold one Colombian superstar to Real Madrid this summer, allowing Rodriguez to join the Spanish giants for a fee that could rise to £71 million.
They are resolved to keep the striker, and club vice president Vadim Vasyliev has reinforced the manager's comments, saying: "For the 2014-2015 season Falcao will be in Monaco."
Monaco are interested, however, in signing Spanish goalkeeper Diego Lopez from Real Madrid. Daniel Subasic started in goal for the French club against Arsenal and Vasyliev was pleased with his performance, but raved about Lopez's ability.
"Subasic did incredible things against Arsenal so I do not think the goalkeeper issue is that important," he said. "But yes, Diego López is a great goalkeeper, one of the best."