The Rams only secured their first win of the Sky Bet Championship season against Norwich at the start of the month, and currently sit 20th in the table.
"Yes he's under pressure but he feels that pressure himself, it's not pressure that we're mounting on him," Morris told talkSPORT.
"I've been in this situation before with poor results and everyone wants good results, but we have a good understanding of what's behind some of the results we've had so far and we're very confident that we have the right plans in place to turn things around."
Rooney is currently a player-coach at Pride Park, and Morris said of the speculation: "We're not even close to discussions of that sort.
"The questions we're talking about is we need better results. Better results come from better performances.
"It's the international break and these tabloids will do anything to get clickbait out there and Wayne Rooney's name is a big carrot for that and I'm sure that's what was behind it."