Mr Trump had been expected to join Mr Giuliani in person at a meeting of Pennsylvania’s senate majority policy committee, scheduled for 12:30pm in a Gettysburg hotel.
On Wednesday morning, however, it was confirmed that the president’s published schedule - which has no travel - would remain.
Mr Giuliani travelled to Gettysburg with Jenna Ellis, a lawyer for the Trump campaign who is also part of what she termed an “elite strike force” of legal representatives.
CNN reported that the president had intended to be there.
The pair last appeared together on Thursday at a press conference at the Republican National Committee in Washington DC, along with Sidney Powell, another member of their team.
Trump’s planned trip to PA is off after a member of the campaign tested positive.
— Kaitlan Collins (@kaitlancollins) November 25, 2020
Mr Giuliani’s son Andrew, who works as an aide to Mr Trump, and Boris Epshteyn, an advisor to the president, were both at the event and have both since tested positive for coronavirus, leading to questions as to whether it was wise for the team to continue to attend in-person events.
The trio claimed that the election had been stolen from Mr Trump by voting machines that switched votes, and were rigged with the backing of Venezuela, Cuba and China.
On Sunday, the Trump campaign issued a statement saying Ms Powell was "practising law on her own" and was "not a member of the Trump legal team".
"She is not a member of the Trump legal team. She is also not a lawyer for the president in his personal capacity," said Mr Giuliani and Ms Ellis in a statement.
Mr Giuliani and Ms Ellis are continuing the fight on their own.
They have now lost 35 of the 43 of the post-election cases alleging election fraud or other irregularities that the president has brought in six states.