Congressman Steve Scalise has undergone another surgery as he recovered from Wednesday's shooting in Alexandria, Virginia.
The source said investigators were not sure of the significance of the names and did not know if it was a list of people Hodgkinson was targeting.
In a statement posted to his Twitter account, Mr Scalise was said to be "more responsive, and is speaking with his loved ones".
For now, Scalise remains in critical condition in the hospital's intensive care unit.
The rifle-wielding 66-year-old, who died during the attack, had a history of anger aimed at Republican officials. He has been sedated, but has been brought out of sedation periodically and been able to recognize and communicate with his family, Sava said.More news: Va. governor: 'There are too many guns on the streets'
More news: Doctors Say Otto Warmbier Suffered 'Extensive' Brain Damage
More news: Tweeting Trump attacks campaign probe 'witch hunt'
This is according to a person familiar with the case who was not authorized to speak publicly and spoke to The Associated Press Saturday on condition of anonymity.
The president said that because of the "tremendous pain and suffering he's now enduring. our country will perhaps become closer, more unified". The gunman, James T. Hodgkinson, was fatally shot by police.
Hodgkinson - an IL home inspector who had been living out of his van near the park - had a social media page filled with criticism of Republicans and the Trump administration. He added that Scalise would be in the hospital "for some time" and would need "a period of healing and rehabilitation" after being discharged.
The update comes just one day after a doctor told reporters here that Scalise is not only expected to walk again but "hopefully run" some time after he is released from the hospital.
"I feel a lot more confident and a lot more optimistic than I did two or three days ago", Sava said. "The Scalise family greatly appreciates the outpouring of thoughts and prayers", the hospital's statement said. Also hurt but released from hospitals were two Capitol Police officers, David Bailey and Crystal Griner, and House GOP aide Zack Barth.