"It's a great project. The design work has been done with cars painted white and carrying the club's crest," Calderon said.
"The agreement is with a team with a good chance of winning and will be for one or two grands prix, but at Montmelo for sure. It will be especially good
fun to see a car racing in Barcelona with a big Real logo on it."
It is well-known that reigning double world champion Fernando Alonso is a big Real fan, and talk of the Liga side sponsoring a car has surfaced before, namely during Juan Palacios' ultimately unsuccessful presidential campaign back in June.
It is the latest stunt in a high profile campaign to link Real with Formula One, with the Bernabeu doors opening early on Sunday to allow fans to watch the Brazilian Grand Prix on giant screens before the eagerly anticipated clasico against Barcelona got underway.
It turned out to be a good day for Calderon, as Alonso sealed his second consecutive title at Interlagos before Real beat their bitter rivals 2-0.
"We had the idea of getting Fernando to dedicate his victory from Brazil to the Madrid fans but it wasn't to be," Calderon added.
"Now we are trying to get him to come and do the honorary kick-off at a match instead."