The Athletic had claimed that Liverpool were close to securing the 16-year-old winger.
"I've said all along my role is to look after the footballers that want to be here," Postecoglou told BBC Sportsound.
"The footballers that don't want to be here? There's another avenue there for them.
"When you look at the starting line-up against Dundee United, there were a few boys who started out as ball boys for our club. You can't tell me they haven't had careers, they've represented their country, they've won trophies.
"There are a couple down south who started here too. People may think going down south is a reward or some guarantee of success. Life, and football in general, shows you there are many avenues towards that goal.
"I think you're in a great place here if that's what your end game is."
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