The press watchdog is investigating the Daily Telegraph's use of undercover reporters to record Lib Dem ministers' thoughts on the coalition government.
It reported comments made by Business Secretary Vince Cable in a meeting with people he thought were constituents.
Lib Dem President Tim Farron asked the Press Complaints Commission to investigate. The PCC said 200 people contacted them over the story.
The Telegraph said it was satisfied it acted within the PCC's rules.
Mr Cable was recorded controversially claiming to have "declared war" on Rupert Murdoch. The remarks led to him being stripped of his powers to rule on Mr Murdoch's bid to take control of BSkyB.
Mr Cable later told his local newspaper the Telegraph had "completely undermined" the work of local MPs. Other Lib Dem ministers taped making unguarded remarks were Norman Baker, David Heath and Paul Burstow.
A PCC spokesman said: "We have now received a letter from the Liberal Democrats asking us formally to investigate. We will do so under clause 10 (Clandestine devices and subterfuge) of the Editors' Code of Practice."
A Telegraph Media Group spokesman said: "The Telegraph always abides by the terms of the Editors' Code and co-operates fully with the work of the PCC.
"We will of course assist their investigation on this complaint in any way we can. We are satisfied we acted within the terms of the code as we believe there is a strong public interest in our publishing this story."