McClennan is seen as one of three contenders to replace Cleary, who on Wednesday confirmed he is heading to Penrith on a three-year deal.
The others are Cleary’s assistant, Tony Iro, and the club’s under-20s coach, John Ackland.
McClennan confirmed he would throw his hat in the ring when applications were called, but was reluctant to comment further.
McClennan, who guided the Kiwis to the 2005 Tri-Nations title in his rookie year as national coach, returned to New Zealand last year after three successful seasons with English club Leeds.
He now works at the Auckland Rugby League, but took time out this month to coach the Exiles to victory over England in an international fixture.
Unlike Iro and Ackland, McClennan is not part of the Warriors’ set-up.
Iro, who is also the Kiwis assistant coach, has served his apprenticeship as first-grade understudy to Cleary for the past two years.
Ackland held the assistant’s job before him, before taking the Junior Warriors to the under-20s title last year.
Chief executive Wayne Scurrah said the club would let the issue of Cleary’s replacement lie for a couple of weeks.