People.com quoted Dr. Gary Erwin of the Baylor Health Care System as saying Monday the hospitalized musician's overall condition has stabilized.
Erwin said Travis is "awake and alert, interacting with his family and friends and beginning to start doing some early physical therapy."
Travis is breathing with the help of a ventilator but hospital staff "hope to have him weaned off of that very soon," Erwin said.
The 54-year-old recording artist underwent an operation last week at the Baylor Heart Hospital in Plano, Texas, to control the swelling on his brain caused by a stroke, a complication of congestive heart failure.
Before the stroke, doctors said Travis was showing signs of improvement.
Travis last month completed his court-ordered rehab stemming from a 2012 drunken driving arrest and was touring again when he was struck down by pneumonia, which led to complications of viral cardiomyopathy and congestive heart failure.