Eleven members of parliament (MPs), mainly Scottish and Welsh nationalists who opposed the war and two opposition Conservatives, want to use the dated practice to force Blair to defend himself at Westminster over his decision to go to war in Iraq.
Although it has almost no chance of success and is likely to be seen as little more than a publicity stunt, the plan will throw the spotlight back on the reasons Blair gave the country for going to war, British newspapers said on Thursday.
The backlash over Iraq has seen Blair's trust rating plummet, and although opinion polls say he is on course to win a third general election expected next year, opponents hope to use the issue to question his credibility.
The impeachment process can be invoked against any person accused of "high crimes and misdemeanours" if a single MP persuades parliament there is a case to answer.
It was last used in 1848 and was last successfully invoked almost 200 years ago in 1806, the newspapers said.
In 1967 a parliamentary committee recommended the right to impeach should be abandoned as "the circumstances in which impeachment has taken place are now so remote from the present that the procedure may be considered obsolete".
"For the prime minister to mislead Parliament and public and get away with it is simply not acceptable"
However, the right was never repealed.
The 11 MPs said they wanted to use the power because they believed Blair acted dishonestly in taking Britain to war by overstating the threat posed by Iraq.
"This will be the first time a group of MPs has taken this step for over 150 years," Welsh nationalist Adam Price said.
"For the prime minister to mislead Parliament and public and get away with it is simply not acceptable."
A top-level inquiry in July cleared Blair of tricking Britain into war but did criticise him for relying on deeply flawed pre-war intelligence.