The Spanish side say they have accepted a £6.45m offer for the 23-year-old right-back, who has just returned from helping Argentina win a gold medal at the Olympics.
Zabaleta joined the Barcelona-based club from his homeland in 2005, helping them win the 2006 Copa del Rey, and has won 5 senior caps for Argentina.
Espanyol said in a statement on their website that Zabaleta is travelling to Manchester today for a medical, adding: "Espanyol have tried to convince Zabaleta to stay in Barcelona, but the defender has shown his determination to continue his career in the Premier League."
The Sun has reported that the arrival of Zabaleta will see Vedran Corluka's proposed move to Spurs go through.