British and Spanish reports confirm that Real's newly-appointed coach Juande Ramos is keen on purchasing a right winger, and Pennant has become a top candidate to join Los Merengues.
According to Marca, Real and Liverpool have agreed a fee over the 26-year-old, but the Spanish giants are yet to finalize contract talks with the player himself.
Pennant is reportedly demanding a salary of 3.5 million Euros a year, while Real are willing to offer him 1.6 million.
The Spanish giants are keeping their options opened, as they are also holding talk with CSKA Moscow to acquire the services of Serbia midfielder Milos Krasic.
However, the Russian outfit set a hefty 20 million Euros price for the player, which minimizes his chances of sealing the move.
Real have been in search for a right flank player since their attempts to sign Manchester United superstar Cristiano Ronaldo failed last summer.
Before joining Liverpool from Birmingham City in 2006, Pennant played for Watford, Leeds United, Arsenal and Notts County.