Democratic presidential candidate John Kerry has said that if he came to power Republican Senator John McCain would be his top choice for defence secretary.
McCain is well liked by both Republicans and Democrats
"I have any number of people that I would make secretary of defence, beginning with our good friend John McCain as an example," Mr Kerry said.
But when asked to respond to Mr Kerry's suggestion, Mr McCain dismissed the idea saying "No thanks, no thanks".
Despite belonging to opposing parties the two men are known to be friends.
Like Mr Kerry, Mr McCain is a Vietnam War veteran and he has a reputation for being a free-thinker who has on occasion been highly critical of President George W Bush.
He lost out to Mr Bush in the 2000 Republican Party primary.
Mr McCain recently sided with Mr Kerry after fellow Republicans criticised the Democratic candidate's commitment to national security.
Such actions have led to speculation that Mr McCain could be a potential running mate for Mr Kerry in the presidential elections due to take place in November.
However, Mr McCain has repeatedly tried to put that speculation to rest, denying that he would ever switch sides to join Mr Kerry's team.
"No, no and no. I will not leave the Republican Party. I cherish the ideals and principles of Abraham Lincoln and Theodore Roosevelt and Ronald Reagan," Mr McCain said on NBC's Meet the Press programme last month.
But Mr Kerry himself has done nothing to quell the rumours, often alluding to an alliance with Mr McCain and even using the Arizona senator's image in an advertising campaign.
Mr Kerry also listed a number of other people he believed would make good future defence secretaries. They included Democratic Senator Carl Levin and Republican Senator John Warner of Virginia, both members of the Armed Services Committee, and former Defence Secretary William Perry.
Mr Kerry made the comments on Wednesday, as he accused the current Defence Secretary, Donald Rumsfeld, of failing to manage the Iraq conflict and the Abu Ghraib prisoner abuse scandal effectively.
"This thing has been so extraordinarily mismanaged and ineptly prosecuted," he said of the photographs revealing that Iraqi inmates suffered physical and emotional abuse at the hands of the US military captors.
Mr Bush has staunchly defended Mr Rumsfeld, describing him as a "superb" secretary of defence.
Repeating a call for Mr Rumsfeld's resignation, Mr Kerry said that the draconian prison policies instituted by the White House in the wake of the 11 September attacks had set the stage for the abuse in Iraq.
He said that Mr Bush and Mr Rumsfeld's decision to not give the suspected al-Qaeda fighters held at Guantanamo Bay, Cuba, the status and rights of prisoners of war had cast an ambiguity over the rights of all US military detainees.