Ed Williams, a spokesman for Thompson in London, said Thompson would not comment directly about the letter. Williams referred instead to comments that he himself had made to Stewart Purvis, a blogger and journalism professor with extensive experience in television news.
In an email to Purvis that was posted on the blog, Williams said it was a "common occurrence" for legal letters to be written at the BBC and reiterated that Thompson had not been aware of the allegation against Savile.
"He verbally agreed to the tactic of sending a legal letter to the paper, but was not involved in its drafting," Williams told Purvis.
Critics of Thompson's role in the Savile scandal found this unconvincing.
Rob Wilson, a Conservative Party lawmaker who has challenged Thompson's explanation, said the former BBC chief had not yet given a "definitive" account of his knowledge about the Savile allegations.
"Now it appears legal threats were issued using his name against a newspaper over claims that he hadn't bothered to read, let alone investigate, but which turned out to be true," Wilson said.
The Metropolitan Police, meanwhile, arrested a man in his 60s on Thursday in connection with the wide-ranging Savile investigation. A police statement said some 450 alleged victims have now come forward.
Associated Press writers Paisley Dodds, Jill Lawless and Cassandra Vinograd contributed to this report.