Sir Alex Feguson's former No 2 at Manchester United is being checked out as a replacement for Dave Hockaday, who was dismissed after just 70 days and 6 games at the the Elland Road helm last month.
Queiroz, 61, has put himself in the frame to become United's ninth boss in 10 years since sliding out of the Premier League after revealing he is keen to return to club management.
The Portuguese, who spent five years in two spells at Old Trafford as Ferguson's assistant, has been Iran coach for the last three years and led them to the World Cup Finals earlier this summer.
He was expected to sign a new deal, but is now instead considering his options.
Queiroz is now a front runner after favourite Steve Clarke ruled himself out to succeed the ill-fated Hockaday.
Former Whites boss Simon Grayson also rejected an Elland Road return so it appears caretaker boss Neil Redfearn will battle it out with the former Real Madrid, Portugal and South Africa manager for the Leeds hot seat.