The Santiago Bernabeu outfit have allegedly put together a bid for the Spanish midfielder as they look to increase the number of options in the Castilla squad
The 21-year-old midfielder, a former Under-19 international for Spain, has been suggested as a strong possibility to bolster the ranks of Madrid's Castilla team after scoring 19 goals for Cordoba in 2011-12.
It is believed that Madrid have offered €1.5 million for Garcia, an offer which still falls short of Cordoba's valuation.
"The only official offer we have received for Borja was from Real Madrid," Carlos Gonzalez told El Diario de Cordoba.
"All the others who are interested in him have called us and said things, but the only offer we have on the table is from Madrid.
"They think he can be an important player at the club, but the fact is that they have not offered a fee which we think is good enough."