The 18-year-old has been linked with some big names in British football.
However, QPR boss Warburton, who spent 19 months at Ibrox as manager, took aim at an agent being busy with it being the transfer window.
The 59-year-old doesn't want too much hype around Armstrong who is on loan at Torquay United in the fifth tier.
"I'd imagine his agent has been extremely busy,” he said. “He's 18 and played eight games for Torquay.
"I'm not being derogatory in any way, I just don't want to put pressure on a young player's shoulders too early.
"Rumours of Celtic and Man City? I'd imagine certain agents have been extremely busy. When you see all these names you just know agents are busy at work in the January window.
"It's absolute nonsense. Let's give the boy a chance now for the next stage of his career."