McGahn played a role in Trump's selection of both Kavanaugh and Justice Neil Gorsuch as candidates for the Supreme Court.
It is not unusual for White House counsels to come and go during an administration.
"I hope it's not true McGahn is leaving [as] WhiteHouse Counsel", the Iowa Republican tweeted, telling Trump: "U can't let that happen".
In a sharply worded tweet earlier this month, Mr Trump said he had allowed Mr McGahn to give testimony to the special counsel.
Citing unnamed sources, Axios said McGahn will leave after Brett Kavanaugh is confirmed to the Supreme Court or after the midterm elections.
The interviews occurred under Trump's last legal team, who opted for a cooperative strategy with Mueller until the president dumped them and brought on Rudy Giuliani for a more combative stance. That McGahn had spent that much time with prosecutors has reportedly alarmed Trump.
In a statement to ABC News, Grassley's spokesman said the senator's tweet reflected his admiration for McGahn's work regarding judicial nominees.
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Sources tell Axios that the main candidate to replace McGahn is Emmet Flood, who joined the White House's legal team back in May and is a former Bill Clinton and George W. Bush lawyer.
Other topics included Mr Trump's comments regarding Attorney-General Jeff Sessions, a frequent target of critical tweets from the President, and the possibility of firing Deputy Attorney-General Rod Rosenstein, who oversees the probe, the Post said.
The White House lawyer reportedly threatened to resign past year because Mr Trump was planning to remove Mr Mueller.
His departure marks the latest of the handful of top aides who worked on the Trump campaign before joining the White House.
"He was surprised", this person said. Flynn was forced to resign after reports revealed Yates' warning to McGahn about Flynn's conduct.
In another showdown in March 2017, McGahn urged Attorney-General Jeff Sessions to not recuse himself from the Russian Federation probe.
The New Jersey native had been a partner at Jones Day, one of the world's largest law firms. He specialized in campaign finance issues after serving on the Federal Election Commission from 2008 to 2013.