It is unclear whether Kelly has actually offered his resignation or whether the president is ready to accept his resignation.
CNN previously reported that a source familiar with the matter said Porter's ex-girlfriend called White House counsel Donald McGahn in recent weeks to inform him of abuse allegations, and added that whatever McGahn did with the information clearly wasn't enough.
That prompted a sharp rebuke from Democrats like Congresswoman Nydia Velazquez, who slammed the White House's "culture of misogyny".
Trump praised Rob Porter's work as White House staff secretary and said he hopes the former aide goes on to a successful career elsewhere.
Sorensen denied the allegations in a lengthy statement to the Post.
Vice President Pence also seemed to draw a tougher line against the former staff secretary than Trump did, telling NBC's Nightly News he was "appalled" by the allegations against Porter.
Porter-who resigned on Wednesday-is reportedly involved romantically with White House communications director Hope Hicks, for whom his second ex-wife, Jennie Willoughby, says she's anxious.
Sorensen's ex-wife reportedly accused him of being violent and emotionally abusive, which he vehemently denied.
Several Trump confidantes reached by ABC News said the president is considering multiple names as possible Kelly replacements, among those, top economic adviser Gary Cohn, Office of Management and Budget director Mick Mulvaney and Rep. Mark Meadows. But White House officials said Kelly pushed Porter to stay in the job even after the release of the photos.
It wasn't until the uproar over the allegations grew and more details surfaced that Porter resigned and Kelly put out a second statement expressing concern about the allegations.
After Nielsen was confirmed and with another deputy chief of staff, Rick Dearborn, expected to soon leave the White House, Carroll quickly took on the duties of a deputy chief - though he was never formally named to the position. Sadly, Trump's support for Porter's and Hicks' silence on the matter is damaging Hick's reputation.
"It was very said when we heard about it, and certainly he's also very sad", Trump continued.
"He said very strongly yesterday that he's innocent", Trump added.
The White House was already under scrutiny this week over its handling of Porter's departure. The president said he had only "recently" learned of the allegations against his former aide and was surprised.
"Of course, I was part of the background check and I was completely honest with what my experience of the marriage, including telling the police instances of abuse or police contact", said Willoughby.