Steinbrenner, a senior vice president for the club, told the newspaper that the Yankees would reach a decision by Monday.
The team could make their selection public in a press conference on Tuesday, pending Commissioner Bud Selig's approval to make an announcement during the World Series. Tuesday would be a potential off-day during the Fall Classic, assuming the the Series goes to a sixth game.
Steinbrenner said that general manager Brian Cashman, who has declined to comment publicly until the managerial search is complete, are in agreement on their inclination regarding who should follow Torre, but the Yankees have been tight-lipped and are offering few clues.
"As far as myself and Brian, there's always been a slight favorite, but only a slight favorite," Steinbrenner told the Times. "Me and Brian have always agreed on who that is. Is Brian's job on the line, depending on who the manager is? The answer is no, because we've always agreed on who is the favorite. The final decision hasn't been made."
With Cashman, whose contract expires after 2008, having direct input, the Yankees held interviews on three consecutive days this week in Tampa, Fla., beginning on Monday with Girardi and concluding on Wednesday with Peña.
Candidates were put through an intensive six-hour process in which they were asked a series of questions, spending time with the club's player development department at the Minor League complex and at Legends Field, the team's Spring Training home.
Candidates also met face-to-face with owner George Steinbrenner, who has gradually ceded some decision-making control to his sons Hank, 50, and Hal, 38, the "young elephants" Steinbrenner has been speaking about allowing "into the tent" for several years.
During that meeting, Mattingly, 46, is said to have impressed management with his passion, conveying how much he wanted to manage the club for which he excelled during a lengthy playing career that began in 1982.
A bench coach for Torre in 2007 and the Yankees' hitting coach for three years before that, Mattingly revealed during a conference call with reporters on Tuesday that he would not have accepted a position on the Yankees' bench before the 2004 season if he had not held an interest in managing.
But Girardi, 43, trumps Mattingly in the category of prior managerial experience, having guided the Florida Marlins to 78 victories in 2006 and beating out the Mets' Willie Randolph for the National League Manager of the Year award.
A hard-nosed former catcher who won three World Series titles with the Yankees, Girardi is said to have an authoritative clubhouse voice, but could also be mulling a potential offer from the Los Angeles Dodgers, according to an ESPN report.
"We're going to pick whoever's the best guy for right now, that's the bottom line," Steinbrenner told the newspaper. "We've got the best baseball people. The Red Sox obviously have some good baseball people, as well, but we've got great baseball people, including some of the guys responsible for the team in the late '90s, one of the greatest teams ever.
"So who am I going to go with? The fans and the media, or the best and the brightest -- the guys that are the smartest baseball people in the country? That's where the final decision's going to be, whether it's Mattingly, Girardi or Peña. The final decision is with ownership, which is the way it should be. But the process Brian set up is spectacular. They really did this right."
Along with the managerial decision, the Yankees also plan to reconvene in Tampa next week to discuss personnel moves, according to the newspaper.
The team wishes to meet with Alex Rodriguez to discuss a contract extension, but will also have to handle several important potential free agents, including Jorge Posada, Mariano Rivera, Andy Pettitte and Bobby Abreu.