The former Real Madrid star has arrived as part of the club's 100th anniversary celebrations this season.
Presa told El Partidazo de COPE: "Five weeks have passed since he played in the Copa America final and he was on vacation, we don't want to put his season at risk. We have to take care of him, he's like a Formula 1 car, he has to last the whole season. It's a source of pride to be able to enjoy James, who is at the peak of his career after winning the Copa America MVP title ahead of Messi, despite losing the final.
"I called him directly a month ago. We have Radamel Falcao as a mutual friend and we saw the possibility of signing him; at the beginning it was difficult but in the end we achieved something historic for Rayo Vallecano: bringing the MVP of the Copa América. We are a humble but ambitious team, like Napoli did with Maradona: nothing similar has been achieved since then."
The Rayo president also spoke about the club's problems: "Vallecas is a very nostalgic, very beautiful stadium, but it is a stadium that is becoming obsolete, that has become small and we need to take another step for the good of Rayo. To be able to celebrate another 100 years we need to find a location that is in line with the fans we have.
"For a match like the one against Barcelona, more than 25,000 people could have entered; we asked for that investment, we didn't do it because the current board is working very hard to pay off a debt that others have created. Now that we see the shore, we don't want to be dragged down again."