According to reports in Spain and Italy, the Argentine's agent Fernando Hidalgo will meet with Real sporting director Predrag Mijatovic on Wednesday.
Real are in search for a striker to cover the absence of Ruud van Nistelrooy, who was ruled out for the rest of the season with a knee injury.
Moreover, agent and intermediary Ernesto Bronzetti affirmed the speculation around Crespo, as he rubbished reports linking Los Merengues with his client Mirko Vucinic of Roma.
"This alleged interest from Real for Vucinic is pure fantasy. Madrid are just after Crespo and then they will swoop for another big name at the end of the season," Bronzetti said on Forzaroma.info.
"Real have offered Crespo a six-month deal with an option for an additional year, but his agent wants two years."
With the presence of Zlatan Ibrahimovic, Julio Cruz, Adriano and Mario Balotelli, Crespo has recently fallen down the pecking order under boss Jose Mourinho.
The former Chelsea player's name was accompanied by that of Egypt ace Amr Zaki in the shortlist of the Primera Liga holders in recent weeks.
Zaki, who is enjoying a magnificent spell with Wigan in the Premiership, is tipped for a bigger move after making immediate impact at the top level.