The subpoena also seeks information about Giuliani's failed attempt to use unfounded conspiracies to justify the seizure of voting machines and about meetings he attended at the Willard Hotel in Washington, DC, where several Trump allies set up a "command center" to discuss options to overturn election results.
When asked about Giuliani and others who invoke attorney-client privilege as a reason why they can not cooperate with the committee, chairman Bennie Thompson said, "that's their opinion."
"We think we're on a healthy footing," added Thompson, a Mississippi Democratic congressman, when asked about a possible legal battle for their testimony.
Giuliani and Powell have both been the subject of sanctions and lawsuits over their efforts on Trump's behalf to bring lawsuits alleging electoral fraud in key battlefield states after the 2020 referendum.
The congressional summonses for Giuliani and Powell are seeking "any and all documents" related to a number of unsubstantiated allegations, according to the source.
These false allegations of widespread electoral fraud include Dominion voting machines that change votes, algorithms used to manipulate votes, dead people voting in elections, Italian satellites used to hack voting systems and voting machines manipulated through smart thermostats controlled by the Chinese government.
The subpoenas also seek "any communication with you that refutes, denies or disputes any allegations of electoral fraud made by you or other representatives of the Trump campaign around the 2020 election," the source said.
CNN's Annie Grayer contributed to this report..