Calderon did not name the new sponsor, which will replace BenQ, the German handset business of Taiwan's BenQ Corp. which has gone bankrupt.
He gave no details of the amount involved.
"Now we have to change sponsor. In a week, we will sign for a sum which is unequaled by anyone," Calderon was quoted as saying by daily El Pais on Tuesday.
Calderon said the sum involved was "unimaginable" for any other club.
Madrid's five-year deal with BenQ, which was due to continue until 2010, was worth Ђ100 million (US$130 million.
Juventus has the current biggest jersey sponsorship contract in world soccer, a five-year deal worth Ђ110 million (US$143 million) with Libyan oil company Tamoil.
Although it is experiencing its worst slump on the field since the early 1950s, Madrid is the world's biggest club by revenue.
The Spanish club increased its income by 17 percent to Ђ275.7 million (US$328 million) for the 2004-05 season, according to the most recent figures.
Last November, Madrid announced the sale of its television broadcast rights to production company Mediapro in a seven-year deal worth Ђ1.1 billion (US$1.43 billion), the most expensive in club soccer, reports AP.
Calderon's announcement of the shirt deal came a week before a court is due to announce whether 10,511 postal votes will count in the result of the club's presidential election last July.
Calderon reportedly could be replaced by a rival candidate.