The heir to the throne is said to have opted for St Andrews instead of Edinburgh although Buckingham Palace insisted no decision would be reached until the 18-year-old receives his A-level results.
Marcus Booth, president of the students' association, said the university would welcome the prince with its "customary warmth".
Mr Booth, 23, who studied medieval history, said: "St Andrews is well used to the place crawling with celebrities, especially when the golf is on.
"I think he would be welcomed as warmly as any other student."
"The union on a Friday night is the only equivalent really to a nightclub environment, but there are 22 pubs and more pubs per square mile than any other university in the country.
The results of the prince's A-level exams, which he took in geography, biology and history of art, are due on Thursday.
The Express newspaper reported Prince William's surprise decision to opt for St Andrews.
The university has refused to comment, saying that it never discusses individual applications.
If the move is confirmed, it would be seen as something of a snub for Edinburgh University where the young prince was expected to go to study the history of art.
The Express reported Prince William made up his mind after paying a low-key visit to the coastal town which is dominated by the university.
Founded in 1411, the institution is Scotland's oldest university.
He is set to embark on the four-year honours degree course after completing his year out to travel around Australia.
British furniture, architecture, Renaissance Italy and modern art are among the topics he will be taught.
It is also reported that the Prince will live in his own accommodation.
If he does attend St Andrews, he will be following closely in the footsteps of previous monarchs.
Many Scottish kings went to the university until the 16th Century.