Knox, 25, and her 29-year-old Italian ex-boyfriend, Raffaele Sollecito, were initially convicted of the crime and sentenced to long prison terms. An appeals court acquitted them in 2011.
Britain's Daily Mirror reported the pair had a secret reunion, publishing photos of what it said was Knox and Sollecito walking together in New York.
The newspaper said the photos were taken Tuesday - the same day Italy's high court harshly faulted the appeals court that acquitted Knox and ordered a new appeals court to consider all the evidence to determine whether Knox helped kill Kirchner.
David Marriott, a Knox family spokesman, said he couldn't confirm the circumstances behind the photos. He said Knox and Sollecito are friends and periodically keep in touch. He said it would be natural for them to visit with each other if they found themselves in the same city.