The RFU has confirmed the Blues have made an enquiry about using the 82,000-capacity home of English rugby should they opt to redevelop Stamford Bridge.
However, Mr Cable, Liberal Democrat MP for the area and Business Secretary, has revealed he too has contacted the governing body to voice his misgivings.
Mr Cable tweeted: "I have written today to RFU about Twickenham Stadium and possible use for a year by Chelsea FC
V serious concerns and need for facts ASAP."
Chelsea announced earlier this summer that they might look to redevelop their stadium, although no timescale has yet been drawn up.
The RFU has previously rejected requests from football clubs to play their fixtures at Twickenham with Fulham's approach in 2001 being rebuffed.
The RFU said in a statement: "We are regularly contacted by a variety of organisations, within and outside sport, on a wide range of opportunities concerning use of what we believe is a world-class stadium.
"We have had an enquiry from Chelsea FC, but have not had any discussions of any substance.
"While we don't comment on any specific confidential conversations, each request is taken on its merit, assessing a variety of factors, such as the effect on the pitch, availability, transport and local considerations and other important implications."
Source : PA
Source: PA