Even as San Francisco 49ers officials spent Tuesday interviewing New York Jets defensive coordinator Ted Cottrell for their head coaching vacancy, they added another prominent name to their list of candidates, while still hoping to name a successor to Steve Mariucci by next week.

Tampa Bay general manager Rich McKay on Tuesday granted permission for the 49ers to discuss the head coaching job with defensive coordinator Monte Kiffin. Neither a time nor a place for the interview has been established and it isn't even clear yet if Kiffin will pursue the job.

The 49ers sought permission to meet with Kiffin almost immediately after the Bucs' victory in Super Bowl XXXVII.

Cottrell spent much of the day Tuesday huddled with general manager Terry Donahue in Los Angeles. ESPN.com has learned that Cottrell technically is no longer under contract to the Jets, having chosen not to exercise an option earlier this month.

It is possible the Detroit Lions, who fired Marty Mornhinweg on Monday, will also want to discuss their opening with Cottrell. There have been preliminary discussions with the Jets on a new contract and it is very likely Cottrell would return to New York as coordinator if he does not land a head coaching position.

A 19-year NFL veteran, Cottrell joined Herm Edwards' staff in New York in 2001. He was instrumental in reversing the fortunes of a Jets defense that began poorly in 2002, in part because of six new starters. Over the final nine games of the year, though, the defense improved dramatically.

The 55-year-old Cottrell, who has been considered in the past a potential candidate for head coach openings, and technically interviewed seven times for vacancies, previously worked in Kansas City (1981-82), Buffalo (1986-89 and 1995-2000) and Arizona (1990-94).

San Francisco has already interviewed Philadelphia offensive coordinator Brad Childress, New England defensive coordinator Romeo Crennel, and incumbent defensive coordinator Jim Mora Jr. Eagles defensive coordinator Jim Johnson got permission to speak to the 49ers but signed a new four-year contract with his current team.

It is believed the 49ers could be interested in one more candidate beyond Kiffin, who further elevated his status as one of the NFL's premier defensive coordinators, given his Super Bowl game plan.

There is a legitimate chance the Bucs will attempt to retain Kiffin with yet another contract extension. Early in the season, Kiffin signed a new two-year deal, through 2004, worth about $1 million annually.

Len Pasquarelli is a senior writer for ESPN.com.