He has required surgery several times since the shooting. The person did not disclose the names, but said those listed had been briefed.
He was in shock and "imminent risk of death" when he arrived, the hospital's chief trauma surgeon said.
In a statement, the hospital said Scalise "continues to make good progress". The hospital reported Scalise was conscious and talking to loved ones.
Scalise's security detail and other police officers shot and killed the assailant, James Hodgkinson of IL, who had lashed out against President Donald Trump and other Republicans over social media.
"We've got to move on, in a sense, that, it means so much to us, to all of us who live there", said Alexandria Sheriff Dana Lawhorne, a Del Ray resident.
The FBI said at a news conference on Wednesday morning that its investigation so far indicates that Hodgkinson acted alone and that investigators have not found a "nexus to terrorism". He is "beginning an extended period of healing and rehabilitation". As I walk across the parking lot to the vehicle, a gentleman approaches me and says, 'Can you tell me, the team today, is that Democrats or Republicans?' I told him it was the Republicans and he said, 'OK, thanks, ' and turned around.
"I came off the field through the gate and right outside is the security detail for the whip".
Scalise's Twitter account posted photos of him with his family over the weekend to mark Father's Day.
Also shot were Capitol Police special Agent Crystal Griner, congressional aide Zachary Barth and lobbyist Matt Mika.
"[Scalise] will require additional operations to manage abdominal injuries and other broken bones".
French defence minister quits over fake jobs claims
Observers say her decision puts more pressure to resign on justice minister Francois Bayrou , the founder and leader of Modem. The ministers' departure gives Macron a chance to reshape his government without including names who could prove awkward.
Georgia special election results
Ms Handel came a distant second to Mr Ossoff in the April election, but the Republican vote had been split among 11 candidates. Williams said he was optimistic about the path ahead for Republicans. "I think that those concerns have only grown over time.