Pakistan are due to shortlist candidates later this week to replace Bob Woolmer, who died at the World Cup in Jamaica in March prompting a police investigation and controversy.
Police this week announced that he died of natural causes, not murder.
Rixon, the former New Zealand coach, told AFP from Sydney that the Pakistan Cricket Board (PCB) did contact him about the role but he had already made other plans.
"I am grateful that they did make contact but at this point of time I have decided to coach private schools in Australia and am not inclined to take an international assignment," said Rixon, who has also been linked to Sri Lanka.
Whatmore was not immediately available for comment.
PCB chairman Nasim Ashraf mentioned both Whatmore and Rixon earlier this week when asked on television about the criteria for Pakistan's next coach.
Ashraf said he was still certain a suitable coach would be found.
"We will shortlist three to four candidates on Saturday and I hope that anyone who might have fears will review his decision," Ashraf told reporters in Islamabad late Wednesday.
Woolmer's death came as a catastrophic blow to Pakistan's already crisis-hit team, which was knocked out of the World Cup by outsiders Ireland the day before the coach's body was found in his hotel room.
Jamaican police initially said he had been murdered and Pakistan's players were fingerprinted and DNA-tested. This week they admitted he had probably died of heart failure.
The popular Woolmer had proved himself successful in a job that has been described the toughest in cricket - with ten different men in charge of the Pakistani side since 1998.
Rixon had previously linked his decision about whether to apply for the Pakistan job to the findings in the Woolmer's case.
"I'm finding it extremely hard to get over the fact Woolmer is no longer with us, to be honest. I'd never say never (to going for Pakistan) but I'll be interested in the result of the inquiry," Rixon said last month.
Besides Rixon and Whatmore, Pakistan also targeted Englishmen Tim Boon and Martyn Moxon for the job.
Ashraf on Wednesday defended his determination to hire a foreigner, saying that players like being coached someone from outside the country.
"We are looking for a young coach with computer knowledge. There is dissent between players and a local coach and a foreigner does not get involved in politics," Ashraf said.
Intikhab Alam, a former Pakistan captain and coach of the team which won the World Cup in 1992, disagreed.
"Politics and infighting are due to weak management," Intikhab said. "Look at what Woolmer did to Pakistan cricket and (Greg) Chappell did to Indian cricket. Total mess."
Chappell quit the India job after Pakistan's arch rivals also flopped at the World Cup, a decision his elder brother Ian said was prompted by Woolmer's death.
All four South Asian cricket teams are currently looking for a new coach after the tournament in the Caribbean, with India having been snubbed by South Africa's Graham Ford and England's John Emburey.
Sri Lanka bade farewell to their Australian coach Tom Moody on a high note after finishing runners-up to Australia at the Word Cup, while Bangladesh said goodbye to Whatmore.
Meanwhile Pakistani batting legend Javed Miandad, who had three spells as coach ending in 2004, was also critical of the selection process.
"If computer know-how is all that matters, then (Microsoft chairman) Bill Gates should have been the best cricket coach in the world," Miandad said.