The Palace of Westminster and broadcasters led by the BBC are currently in discussing the prospect of lifting the ban, the paper said.
In 2007, a clip of Gordon Brown picking his nose became a mini-YouTube hit, registering over 470,000 views. Westminster authorities have periodically asked for such clips to be removed.
Under current rules no website, except the official Westminster site, is permitted to broadcast parliamentary proceedings. Although MPs can upload clips of their speeches online they are expected to prevent third parties from embedding these clips.