Mr Graham, a South Carolina senator, suggested it would be beneficial for Mr Trump himself to attend the 20 January swearing-in ceremony, as previous presidents have traditionally done.
His comments came as officials in Arizona and Wisconsin confirmed Mr Biden as the election winner, dealing another blow to team Trump's so far fruitless attempts to delay the certification of results in key battleground states.
Lawyers for the president appear powerless in preventing the electoral college (EC) from officially confirming Mr Biden's win when it meets on 14 December.
The former vice president is projected to win 306 EC votes, far more than the 270 required to enter the White House. He has also won the popular vote by over 6 million votes.
Speaking to reporters on Monday, Mr Graham refused to publically acknowledge Mr Biden's victory, citing the outgoing president's false claims of voter fraud.
But he did concede that Mr Trump's attendance at the January inauguration could go some way in helping to heal America's bitterly divided political landscape.
"If Biden ends up winning, yeah I think so," said Mr Graham when asked if the defeated incumbent should show up to the ceremony.
"I think it's good for the country, it would be good for him [Mr Trump]. I hope Biden comes to his," Mr Graham added with a hint of sarcasm in his voice.
The confirmation of Mr Biden's win in both Arizon and Wisconsin came just days after a Pennsylvania federal court dismissed team Trump's legal challenge to the election result in the Rust Belt state.
With just two weeks to go until the EC meets, Mr Trump's legal team is fast running out of road in its efforts to overturn the result of an election they falsely claim was "stolen".
Despite that, a large number of GOP lawmakers - Mr Graham among them - continue refusing to recognise Mr Biden as the election winner.
Capitol Hill observers say those backing the president are only doing so out of fear and so as not to upset a portion of their electoral bases.
Alaska senator Lisa Murkowski is among the sitting Republicans to come out and call on the president to admit defeat.
“I think he should concede. I think the race is over,” she told CNN’s Manu Raju on Monday.
Mr Trump appears to have no plans to throw in the towel and continues using Twitter to push his unproven allegations of ballot irregularity, erroneously claiming the election was "rigged".
It remains to be seen whether or not he will attend Mr Biden's inauguration.