The members of the billionaire’s administration are two of the most visible staffers in the presidential building.
Mrs Sanders is understood to have told friends she plans to depart at the end of the year.
Meanwhile, Mr Shah is also considering his leave, but no exact date has been confirmed.
Mrs Sanders is currently serving as the White House press secretary while Mr Shah is the principle deputy press secretary.
A former official told CBS News further exits are expected in the White House’s communication department in the next few weeks.
The source said: “There will be even more people leaving the White House sooner rather than later, laid off or just leaving out of exhaustion.
“And it is going to be harder to find good people to replace them.”
They added the Trump administration will have a “harder time” bringing in a new wave of staff because it will struggle to bring in “loyalists”.
The source continued: “I do think they’re going to have a harder time getting the second wave of people in than the first, because those people were loyalists, and new folks will have to be recruited and encouraged and then survive the vetting process.
“In addition to all of that, the President prefers to have a small communications staff.”
Senior fellow at the Brookings Institution, Kathryn Dunn Tenpas, stated the vast number of departures in high levels of the Trump camp shows “troubling inconsistency”.
She stated: “So many people haven’t even stayed in these jobs to master the learning curve.
“You don’t hear much about the importance of expertise.
“This is a White House that doesn’t seem to value that or understand the consequences of it.
“It’s kind of one of those things where we may not know the vulnerability of lacking expertise unless there is a crisis — or a crisis that may have been averted had a person been in the room.”
Another source emphasised the slew of exits risks the Trump administration bringing in replacements that “aren’t qualified”.
They explained: “Nobody wants to come in.
“So they’ve gone through two rounds and now they’re at third tier of people who are just lucking out — battlefield promotion ends up promoting people who aren’t qualified for the position.”
It is understood Mrs Sanders developed a close relationship with the Republican firebrand after the departure of Hope Hicks, the White House’s former communications director.
Several other high-profile communications staff have left the administration in recent months with Josh Raffel, the top communications aide of Jared Kushner, and National Security Council spokesman Michael Anton helping to form the list of departures.