Ranieri's opposite number at Real Madrid, Carlos Queiroz, also finds his position under threat.
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Old Trafford insiders credited Queiroz with meticulous preparation, modernising training and re-organising United's defence.
Queiroz says Giggs has a "special sense of humour - very accurate, quick and sarcastic".
The loss to already-relegated Murcia heaped further pressure on Real coach Carlos Queiroz.
"Scoring goals always improves confidence, " said Queiroz, whose side face Brazil on Friday.
Queiroz is reported as saying he will wait until after the weekend's league matches before unveiling his squad for Bosnia.
"It was really unusual to see a couple of our players playing so slow, without tempo and making mistakes, " added Queiroz.
Queiroz also insisted United's players must stay in hotels before every domestic game, a ploy Ferguson admitted his players thrived on.
They are a point behind leaders Valencia and should they fail to win the league, Queiroz seems unlikely to keep his job.
BBC: SPORT | Football | My Club | Chelsea | Chelsea eye Real duo
Queiroz hopes United will bounce back from this setback by beating Arsenal.
Congress also began impeachment hearings on Wednesday for deputies Sandro Mabel of the Brazilian Liberal Party and Romeu Queiroz of the Labour Party.
We got to speak with Google TV's VP of Product Management Mario Queiroz today, and he shared a couple of tasty tidbits with us.
Queiroz made such an impact in his first spell at United, which lasted 12 months, he even managed to earn praise from Roy Keane.
Rerunning his calculations, Mr Queiroz found that, together, these would cause the pensions payroll tax in 2050 to rise to 40% (still a daunting figure).
"We believe the team was affected by international call-ups, " said Queiroz.
Queiroz admitted that United had played well below their usual form.
"From now until Sunday a lot of things can transpire, with Ronaldo as with other players, " Queiroz is reported as saying in Correio da Manha.
Portugal coach Carlos Queiroz made four changes to the team from Monday with Pepe and Ricardo Costa coming into defence, and Danny and Duda in midfield.
Michael Ballack scored a late penalty for the Blues but Queiroz feels Ballack should have also conceded a penalty for an apparent foul on Cristiano Ronaldo.
Queiroz, however, believes Ronaldo should be made available, with reports claiming he will ask to have Ronaldo examined by a federation doctor to assess his fitness.
"I would like to express my great satisfaction to my players for the wonderful way they played, their great attitude, their reverence to the game, " said Queiroz.
According to Bernardo Queiroz of the Federal University of Minas Gerais, without reforms, by 2050 they would have to reach a crushing 86% to keep the system going.
Queiroz made his name as the guiding hand behind Portugal's so-called "golden generation" of youngsters including Rui Costa, Joao Pinto and the man he will rejoin at Real, Luis Figo.
Mr Queiroz says the lesson from abroad is that once those in or near retirement are very numerous, reform becomes so urgent that it will have to hit them too.
Real's poor season means that there has been speculation Queiroz himself will be forced out in the summer but the ex-Manchester United assistant manager says he intends to stay with Madrid.
United boss Ferguson did not want Queiroz to leave in the first place and he, along with the rest of the club, will be glad to see him gracing their corridors again.
Queiroz was regarded as a success with Bafana Bafana before quitting for United and, after his ill-fated spell with Real, is now he is back to help steer United to glory once more.
However, Queiroz insisted that United will not falter in their pursuit of the league title and says it is vital the club now supports the players after what he perceives as recent injustices.
He even handed Queiroz the tactical credit for the 2-0 win over Arsenal at Old Trafford that kept the title race alive, with his suggestion of Phil Neville in a holding role a master-stroke.
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