The Colombia stars have been linked with moves to La Liga giants Barcelona and Real Madrid, but the club's vice president says there have been no negotiations
With five goals in four games, James has emerged as one of the stars of the World Cup and his performances have led to links with Spanish giants Real Madrid and Barcelona, while compatriot Falcao has also been rumored to be on the move to Carlo Ancelotti's side.
However, Monaco chief Vasilyev insists neither Colombia star has been subject of transfer talks with the principality outfit this summer.
"There are no negotiations with any club for Falcao," he told a press conference on Thursday.
Recent speculation suggested Falcao requested a transfer but the Russian denied this was the case, adding: "We have not talked about that. We count on him and believe he will have a great season in 2014-2015.
"Nobody is not transferable, I don't know of any examples in football - yet there is no discussion, we rely on him."
Though Falcao missed the World Cup because of a serious knee injury, James has shone for Colombia, which faces Brazil in the quarterfinals on Friday.
And Vasilyev believes the 22-year-old's displays for Jose Pekerman's side have justified the 50 million euro fee Monaco paid Porto last summer.
"Everyone was surprised at the large sum we spent last year and now everyone is talking about him. That means that we were right," he added.
"We strongly believe in this player, it is very important to us, he still has four years on his contract and we will do many great things together."