That puts the Conservative prime minister at odds with his Liberal Democrat deputy, Nick Clegg, The Guardian reported. Clegg argues all three major parties promised more reform of the upper house in the 2010 campaign, making another vote unnecessary.
"My view is that you shouldn't rule it out," Cameron said Monday in an interview with the BBC.
Cameron urged political parties to "work together, rationally, reasonably, sensibly."
The Labor Party threw most hereditary peers from the House of Lords in 1999 but took no further steps toward reform. Under the plan backed by Clegg, most members of the Lords would be elected to 15-year terms and could not run again, and the size of the house would be cut from about 800 to 450.
The house includes a small group of Lords Spiritual, senior leaders of the Church of England, 92 hereditary peers and almost 700 life peers. The life peers are a diverse group, including business executives, former government ministers and scientists -- and two female mystery writers, Baroness (P.D.) James of Holland Park and Baroness (Ruth) Rendell of Babergh.
Notable deaths of 2014 [PHOTOS]