George Papadopoulos, an aid for the Republican Party Presidential frontrunner, said it would be "wise" for Cameron to "reach out in a more positive manner" to Trump.
This comments come after Cameron lambasted Trump's plan to implement a "total and complete shutdown of Muslims entering the United States" in December.
While debating a petition calling for Trump to be banned from entering the UK, Cameron said:
"I think his remarks are divisive, stupid and wrong. If he came to visit our country I think he would unite us all against him."
The prime minister refused to back down from his comments during a recent press conference with US President Barack Obama, however Papadopoulos told the Times newspaper that Trump would welcome any sort of approach from Cameron.
"First we need an invitation. Of course if the United Kingdom extended an invitation it would be a tremendous show of unity and a wonderful spectacle […] That invitation has not yet been extended… but if it is it would be received in a positive way."
When asked if Mr Trump would forgive Mr Cameron's comments, Mr Papadopoulos said:
"I can't speak directly for him but it would seem that if Prime Minister Cameron is serious about reaching out, not only to Mr Trump's advisers but to the man himself, an apology or some sort of retraction should happen."
"To see Mr Cameron come out as the most vocal opponent was uncalled for. Considering that we believe that the UK-US relationship should be a cornerstone, not just of NATO policy but elsewhere, it would be wise for him to reach out in a more positive manner to Mr Trump."
While many general citizens and Republican Party members have been shocked by Trump's comments and rhetoric throughout his campaign, his popularity continues to rise, with the 69-year-old business tycoon expected to take on Hillary Clinton in the US Presidential elections in November.