Doug Richard, 57, is accused of engaging in sexual activity after contacting her through a website.
He denies sexual activity with a child, causing or inciting a child to engage in sexual activity and a charge of paying a child for sexual services.
Mr Richard, of Islington, north London, is due back in court for a trial  scheduled to start on January 25.
The US-born businessman, who is on unconditional bail, entered not guilty pleas during a short hearing at the Old Bailey.
The millionaire, who appeared on BBC's Dragons' Den in the first two series, has also advised David Cameron on support for small businesses.
A former panellist on Dragon's Den has denied paying a 13-year-old girl for sex after meeting her online.