The 32-year-old took to Twitter and said that she has not been romantically involved with the footballer, who is married to popstar-turned-designer Victoria Beckham, reported Contactmusic.
"Dear Twitter friends, I have read some horrible rumours on here and want you to know I absolutely deny I have had an affair with David Beckham," she posted.
"The rumours are very hurtful, untrue and my lawyers tell me actionable. I have only met David twice: once at the Military Awards in 2010 and 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," Jenkins added.
The singer split from TV presenter fiance Gethin Jones in December last year.
A spokesman for David also denied the buzz, saying, "We have to deal with this type of nonsense all the time on Twitter. One minute David is dead, then you have to deal with more scurrilous rumours. There is not one jot of truth to any of it."