Whether Trump or Biden wins in November, Beijing will be hoping to reset the US-China relationship

 George W. Bush warned Barack Obama that "the critics will rage (and) your 'friends' will disappoint you," while Obama urged current US President Donald Trump to "sustain the international order that's expanded steadily since the end of the Cold War."

Anyone looking to advise the occupant of the Oval Office in January -- whether that is incumbent Trump beginning a second term, or a new President Joe Biden -- would do well to urge them to focus on the US relationship with China, which has cratered during Trump's time in office.

Indeed, the President who takes the oath of office in 2021 may be the first in two decades whose biggest foreign policy challenge is not the wreckage left by Washington's twin invasions of Afghanistan and Iraq, but dealing with a new, multipolar world order where the US is no longer the sole superpower.

China currently challenges the US for position as the world's largest economy, and, with a massively expanded and emboldened military, threatens US forces or their allies in a number of potential hotspots. Observers have warned of a new Cold War, or even the potential of open conflict or proxy battles between the two powers.

Under Trump, Washington hit China with trade tariffs, sanctioned Chinese and Hong Kong officials, and stepped up aid and support for the democratic and self-governing island of Taiwan. This year has seen Trump repeatedly blaming Beijing for the coronavirus pandemic, and the shuttering of consulates in both the US and China.

Beijing, for its part, will be looking for a reset in January no matter how the election turns out. China's leaders have not appreciated being a talking point in that contest, which has exposed how hawkishness towards Beijing is increasingly the cross-party consensus in Washington.

Ryan Manuel, managing director of Official China and an expert on the Chinese leadership, said relations with the US are "the personal responsibility of (President) Xi Jinping and he's already been criticized internally about the deterioration in affairs."

"The Chinese system at the moment has been told to wait and hold, and only act exactly in proportion to what the US does," Manuel added. "Once the election is over the push for a reset will begin."

Speaking earlier this month, Cui Tiankai, the Chinese ambassador to Washington, said Beijing has been "firmly opposed, all along, to a new 'Cold War' or decoupling, and we are committed to the sound and stable growth of China-US relations."

"The China-US relationship is experiencing severe difficulties rarely seen in the past 41 years of diplomatic ties," Cui said. "This has seriously undermined the fundamental interests of the Chinese and American people."