"Two Premier League clubs have been monitoring him this season but they have gone about it correctly so they will remain nameless," Kinder told the Carlisle News & Star.
"There has been no approach from any other club about Gary and we want it to stay that way.
"Someone is just rumour-mongering with Newcastle being his hometown club. This sort of speculation doesn't help. We want him to stay and develop with us because he has still got a lot to learn."
Madine has scored 19 times for Carlisle's youth side.