Saif al-Islam studied at the LSE from 2003 to 2008, gaining both a Master of Science degree and a doctorate.
But allegations have emerged that he used a ghost writer, and copied sections of his thesis.
In 2009, he pledged a £1.5m donation to the LSE from the Gaddafi International Charity and Development Foundation.
The LSE’s involvement with the Libya prompted student protests last week.
In a statement, the university said: “LSE is aware that there are allegations of plagiarism concerning the PhD thesis of Saif Gaddafi.
“The School takes all allegations of plagiarism very seriously, and is looking into the matter in accordance with standard LSE procedures.”
Embarrassment
He said the decision to accept research funding from a foundation controlled by Saif Gaddafi had “backfired”.
The LSE’s ties with Saif al-Islam Gaddafi, a son of the Libyan leader, are proving to be controversial
Sir Howard, who is a former head of the Financial Services Authority (FSA) and deputy governor of the Bank of England, said the decision to accept £300,000 from the Gaddafi International Charity and Development Foundation had been debated “extensively” within the LSE.
Last week the university said it was reconsidering its links with Libya “as a matter of urgency.”
But that did not appease angry students.
Last Wednesday a dozen students stormed his offices, demanding the £300,000 of the £1.5m donation already accepted be “paid back” to the Libyan people.
There were also protests outside the School, as students gathered to express their concerns.