The prime minister will hold informal talks with the US leader - and the leaders of Canada, Poland and Ireland - on Sunday.
She will meet her Australian and New Zealand counterparts on Saturday.
Monday's funeral will be one of the biggest diplomatic events of recent years, with some 500 heads of state and foreign dignitaries expected to attend.
It will provide Ms Truss with an opportunity to meet foreign counterparts less than two weeks after taking office.
Downing Street added that further meetings to take place over the weekend could be fixed later on Friday.
Although she met Mr Biden when she was foreign secretary, this weekend's meeting with him will be Ms Truss's first as UK prime minister.
No 10 said the meeting would take place in Downing Street on Sunday, along with meetings with Irish Taoiseach (Prime Minister) Micheál Martin, Canadian PM Justin Trudeau, and Polish President Andrzej Duda.
Before this, Ms Truss will also meet Australian PM Anthony Albanese and New Zealand PM Jacinda Ardern on Saturday at Chevening, the foreign secretary's official country retreat in Kent.
Ms Truss will also attend the UN General Assembly in New York next week, where further meetings with global leaders are expected.
Downing Street said the talks this weekend would not be formal bilateral meetings because of the official 10-day mourning period, meaning there would be no media access.
The media will not receive summaries of the discussions as would normally happen after the PM's meetings with foreign leaders, No 10 added.
The meeting with Mr Martin comes at a time of strained relations with the EU over post-Brexit checks in Northern Ireland.
The UK is refusing to apply some of the checks it signed up to in the Brexit withdrawal deal, prompting a series of lawsuits from the EU.
Mr Martin has expressed concern about legislation Ms Truss introduced as foreign secretary enabling the UK to alter the legal commitments it signed up in the exit treaty in 2019.
Ms Truss is expected to meet European Commission president Ursula von der Leyen for talks at the UN meeting in New York next week.
The state funeral service in Westminster Abbey on Monday is expected to be attended by hundreds of foreign dignitaries, including politicians and royalty.
Syria, Venezuela, Afghanistan, Myanmar, Russia and Belarus have not been invited - whilst Iran, North Korea and Nicaragua have been asked to only send a senior diplomat.
A high-ranking official from China had been expected to attend, but a Chinese foreign ministry spokeswoman said earlier no decision had been made.
It comes after a delegation of Chinese officials was barred from attending the lying-in-state of the Queen in Westminster Hall.
According to parliamentary sources, Commons Speaker Sir Lindsay Hoyle refused a request for access over Chinese sanctions against five MPs and two peers.
Sir Lindsay told the BBC: "It's better I don't comment because everything has security implications. It would be wrong of me to do so."