Washington (CNN) White House chief of staff John Kelly did not formally tender his resignation to President Donald Trump on Friday, but he did make clear that he would resign if the President wanted him to, a source with knowledge of the matter told CNN.

Talk of Kelly's viability as chief of staff reached a fever pitch on Friday afternoon amid intense scrutiny surrounding the handling of domestic abuse allegations against White House staff secretary Rob Porter, who resigned Wednesday while denying the allegations against him.

White House deputy press secretary Hogan Gidley adamantly denied that Kelly had offered to resign in any way.

"He has not offered to resign," Gidley told CNN Friday.

While the source said there was no indication on Friday that Trump would ask Kelly to resign over the matter, another source told CNN's Gloria Borger that Trump has been asking friends and associates over the phone about various potential replacements for the chief of staff position.

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