Briton Irvine and Spain's De la Rosa will be be replaced by Australia's Mark Webber from Minardi and Williams test driver Antonio Pizzonia of Brazil, the tabloid said.
Irvine, the oldest driver in Formula One at 36, was out of contract at the end of this season, but De la Rosa had one year left on his contract at Jaguar.
Irvine has long been expected to be replaced by Webber, and Pizzonia put himself in the frame for a drive with an impressive test for the team before the end of the season.
But if Jaguar have dropped De la Rosa, they will have to pay him off.
Jaguar boss Niki Lauda was unable to confirm when his driver line-up would be announced.
"I don't know when we will get it sorted, but I hope it is within the next few weeks," the Austrian said.