The 'outing' of the agent was seen as retaliation against a critic of the Iraq war.
"The president has had discussions with an outside attorney, and in the event that he needs advice he would retain him," said White House spokesman Allen Abney on Wednesday, naming the lawyer as Jim Sharp.
A federal grand jury has been hearing testimony since January from administration and government officials in an attempt to establish who leaked the name of CIA operative
Valerie Plame to the media last year.
Plame is the wife of Joe Wilson, a former ambassador who was asked by the CIA to travel to Niger in February 2002 to check reports that Iraq had tried to buy enriched uranium from
the African country.
Wilson rejected uranium claims
Wilson dismissed the reports as unfounded, but Bush nevertheless included a reference to the supposed deal in his State of the Union speech in 2003, citing it as one of the reasons to invade Iraq.
The CIA later acknowledged that the uranium reports were based on forged documents and the White House said they should not have been mentioned in the State of the Union speech.
A newspaper columnist disclosed Plame's identity in July last year and Wilson accused the Bush administration of having leaked the information to pay him back for having publicly
taken issue with the president's uranium claim.
It is illegal under US law to disclose the name of a covert agent who has served outside the country in the previous five years.
Reports that Bush had contacted an attorney were first carried on Wednesday by CBS News.