The 47-year-old rap icon and the chart-topping Brit spent time together at a bar in New York City just before Amy died of alcohol poisoning in July 2011, and Jay even invited the 'Back to Black' hitmaker to stay with him because he was so worried about her declining health.
Recalling their conversation, Jay - who is married to fellow musician Beyonce - said: ''I was like, 'You don't even stutter. Why are you doing that?'
''I looked at her, and I was like, 'Stay with us.' The first time we hung out, I told her, 'Stay with us.'''
At the time, Amy - who battled drink and drug abuse for years - was being implored by people around her to attend rehab in order to get her issues under control.
And Jay was shocked the singer-songwriter was so reluctant to address her problems.
Speaking to Tidal's Rap Radar podcast, he shared: ''She was telling us, she was writing the songs to our face. 'They're trying to make me go to rehab, I'm not going,' like, what? You have to go!''
Amy was found dead at age 27 in her London apartment, with an expert subsequently finding that she had a toxic amount of alcohol in her system.
Meanwhile, during the podcast, Jay also stressed the need to talk more openly about mental health issues in light of Chester Bennington's suicide in July.
The New York-born rap star and Chester - the lead singer of Linkin Park - collaborated together on their 'Collision Course' album in 2004.
Reflecting on the situation, Jay explained: ''We're not dealing with that because it's not the cool thing to do.
''These things unfortunately have to happen on a large stage so everyone can see.''
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