The classical singer says she has not been romantically involved with the soccer player who is married to Victoria Beckham.
Online gossip even claimed he had taken out an injunction to prevent details of the ''cheating'' leaking to the press.
In a series of tweets Katherine, 32, wrote to her 225,000 followers: ''Dear Twitter friends, I've read some horrible rumors on here & want u 2 know I absolutely deny I've had an affair with David Beckham.
''The rumours are very hurtful, untrue & my lawyers tell me actionable.''
She went on to insist she has never even been alone with David.
She continued: ''I've only met David twice: once at the Military Awards in 2010 & on a night out in the West End in Feb 2012.
''We were out in a group of friends & it was just a normal fun evening out. Just so we are clear I have never been on my own with him and never arranged to meet up.''
The rumors appear to come from Australian magazine Famous, which printed a story in its latest issue claiming the Beckhams had split.
It said Victoria had broken down during a recent London lunch with friends after they told her the 37-year-old sportsman had grown close to Katherine.
A spokesperson for the Beckhams said the couple felt hurt by the allegations.
They said: ''It's absolutely untrue and the worst in hurtful, damaging media gossip and rumour.
''Legal letters have been sent to the magazine in question.''