Kuol has been very impressive in the A League in Australia, netting four goals and providing an assist in ten games for the Mariners.
Now he is being linked to giants like Newcastle and Barcelona in Europe.
Speaking on The GegenPod, Schwarzer had some advice for Koul about moving to Europe too quickly.
He said: "Get your head down. Don't get sucked in by all the attention, don't let your head get pulled up into the clouds. Wherever you go, even if it's a big club or a small club, keep doing the basics.
"Keep doing the right things because we've seen it with players leaving Australia in the past and they'd thought they'd already made it when in fact they'd gotten nowhere near it and after a couple of years, they fell by the wayside.
"Just because you're a talent at this age doesn't mean it'll last forever. I'm the first person to say 'Go to Europe' - if you're good enough to make it in Europe, that's where you'll want to be. But that's where the hard work starts - it's hard to get there but it's even harder staying there."