Norris, who will be 34 later this month, made almost 250 appearances for the Pilgrims between 2002 and 2008 and is looking for a new club having left Leeds on Monday but Argyle boss John Sheridan says they are not interested.
"It's just speculation," he told the Plymouth Herald. "He was a good player when he was at Plymouth.
"It's a name that people know, but he's not someone who I'm interested in."