The Colombia hitman has been linked with a number of clubs in the transfer window, with the 28-year-old rumoured to be seeking a move away from the principality.
However, on the eve of the new Serie A season, Marotta is adamant that The Old Lady wil not be making an offers, and he is happy with the current crop of talent.
"There are many rumours, but there has been no meeting," Marotta told Sky Italia.
"There is nothing concrete. We are already competitive for our aims.
"We need to be realistic that this is not within our possibilities."
Monaco vice-chairman Vadim Vasilyev also believes that Falcao will remain with Monaco.
"I really hope he (Falcao) will be present," Vasilyev told a press conference.
"But I really believe he will."