Reports on Tuesday suggested that the Foxes had made a £1.5million bid for the 22-year-old Canada international, who scored 21 goals for the Gills last season.
But, speaking after Tuesday night's 4-2 friendly win over Dartford, Stimson said: "We've had nothing at all from Leicester, it's just paper talk. We don't want to lose our better players but at the end of the day every player has got his price I suppose.
"No-one has made an enquiry to me and I don't think the chairman has had any phone calls which is pleasing because he's someone who even in these pre-season games would be vital to us because of the way he plays."
Stimson believes the talk will not affect his star striker, who is currently away with Canada at the CONCACAF Gold Cup, where he has already helped his country through to the quarter-finals.
He added: "I'd be amazed if it went to his head because like I've always said, the kid is a model pro. I don't think it will faze him at all, if anything it will just probably give him another pat on the back and say 'people recognise I'm worth some money' and rightly so. I won't mention it to him, I've told him if anyone makes any enquiry he will be the first to know."