If the new contract is finalized, "Big Papi" would earn an average $12.5 million per year from 2007 to 2010.
"David will get more than $50 million if he signs this extension, which would run until 2010," said the source.
"He is very happy, although there are still some details that need to be worked out," added the source.
A representative of the SFX agency, which manages Ortiz, declined to provide details of negotiations with the Red Sox.
"We're negotiating, that's something everyone knows, but we're still not prepared to make any kind of announcement. There's no deal yet," Fitzgerald Astacio told ESPNdeportes.com.
Since he joined Boston from Minnesota in 2003, Ortiz, 30, has become one of the most productive players in the Major League Baseball.
The designated hitter has 119 home runs and 388 RBI in three seasons with the Red Sox.
Ortiz was voted MVP of the AL Championship Series in 2004, when Boston came back from an 0-3 deficit to defeat the Yankees in seven games and advance to the World Series. The Red Sox then swept the St. Louis Cardinals for their first title since 1918.
Ortiz will earn $6.5 million in 2006, the second year of a two-year, $12.5 million contract signed in May 2004. The team has a $7.7 million option on him for 2007.
He has been asking for an extension since the winter break started.
Last Tuesday, Ortiz said he would leave negotiations in the hands of his agents and that he wouldn't take an active part in the process.
Enrique Rojas is a reporter and columnist for ESPNdeportes.com and ESPN.com.