The library was opened by King George V in 1934
A Cambridge University professor has warned it is heading for "dangerous territory" by offering to rename its main library for a major donation.
The university is seeking a substantial endowment for the library amid a long-running campaign to raise £1bn.
Prof Gill Evans said there had not been a consultation and she feared for the library's "academic integrity".
A university spokesman said it was "standard practice" to name buildings after benefactors.
He added it was not yet in discussions with any library sponsor.
'Great research library'
The university has not revealed a value on the honour of naming the library, which houses some of the most important collections and manuscripts in the world.
The university has raised £800m over nine years, some of which has helped boost its collections, buildings, student accommodation teaching, and the library.
"Cambridge University Library, like all similar institutions, regularly explores the full range of funding opportunities open to it as it seeks to maintain its position as one of world's great research libraries," he said.
"Securing a substantial permanent endowment for the library remains a high priority.
"However, any proposal for a major benefaction... would be subject to the normal stringent university approval processes."
'Money with strings'
A link on the library's website states: "Oxford has its Bodleian, Harvard has its Widener, Yale has its Beinecke, Manchester its Rylands.
"In Cambridge, the university library is one of few such institutions of equivalent stature in the western world that remains un-named.
"This represents a unique opportunity to recognise an exceptional and transformative benefaction in perpetuity."
But Prof Evans, emeritus professor of medieval theology and intellectual history, believes the deal could mean "money with strings" for the university, while the ideal benefactor would willingly give without a "reward".
Some of Darwin's correspondence is housed at the library
She also said the university must protect the library's "academic integrity".
"Sponsorship can mean branding and logos and sponsors always want commercial advantage," she said.
"Universities have to keep their hands clean or they can't do their job."
Cambridge University Library was established in the 15th Century, with the current building opened by King George V in 1934.
It has 100 miles of shelves, which extend by two miles every year, and two million books on open stacks - the largest open access collection in Europe.
Its special collections include the papers of Isaac Newton, an archive of Charles Darwin's correspondence and a copy of the Gutenberg Bible from 1455, the earliest European example of a book produced using moveable type.
Recent examples of renaming buildings at the university in return for substantial donations include Murray Edwards College, formerly New Hall, and the switch from University College to Wolfson College.