I believe the correct term would be off his port quarter.
In my experience, diesel/electrics are reaallly quiet. In stock DW, I've gotten within 2 or 3 nautical miles of a Kilo without even knowing it. I was in a Seawolf and I didn't see anything on my sonar. If you're pretty confident it's only you and the Kilo out there, you may want to try active search. But even then, it's always worrisome to give away your position if you don't have to. It's tricky for sure.
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