The 52-year-old frontman has been battling COVID-19 - a virus that has already killed over 38,000 people worldwide since December - for over a week in a hospital in upstate New York and is now relying on a machine to help him breathe.
Speaking to Variety.com, his lawyer Josh Grier has denied the 'Stacy's Mom' hitmaker is a "coma" but explained: "He's very sick and is heavily sedated, as are all people on ventilators, but no one has used the word 'coma' to me."
Mr Grier added that the 'Crazy Ex-Girlfriend' songwriter has been receiving "excellent care" since his admittance last week but doctors were reluctant to make any predictions about his recovery because so little is known about the disease.
Adam's cousin Jon Bernthal has since taken to his social networking sites to wish his relative a speedy recovery and asked his fans to keep him in their "heart."
The 'Walking Dead' star wrote on Twitter: "This is my big cousin Adam. As a little boy I would be mesmerized by his talent. He showed me how cool it was to be an artist. We love you Cuz. Stay strong. Bless you and all of the heros at the hospital on the front line. Please keep Adam in your heart. (sic)"
Adam and wife Katherine Michel, who got marriedin 1999, have two daughters together, Sadie and Claire.
Since the coronavirus - which originated from Wuhan, China, and can cause a high temperature and continuous cough in those infected - began to spread around the world, many celebrities have tried to raise money for relief funds.
Blake Lively and her husband Ryan Reynolds recently made a $400,000 donation towards the fight against coronavirus - just two weeks after they handed over a seven-figure sum to foodbanks in North America.