The Argentine is believed to be interested in a January move in order to get more first team action.
Real are desperate to strengthen their team up front as Ruud van Nistelrooy will be out of action for the rest of the season with a injury.
Spanish newspaper AS says Real have offered Crespo a contract until June 2009.
Reports suggest the 33-year-old wants a deal that will keep him with the Spanish giants until 2010.
