Tier 2 general to ILR Conversion

I have a question. I was on student visa from September 2014 to January 2016 and then converted to tier 2 general on about 10th Feb 2016. I switched job to another company with a new tier 2 general visa in September 2017 and the current visa expires in September 2020. Technically I may apply for my ILR on about 15th Jan 2021 .
My question is that can I apply for ilr in September 2020 ? Or do I need another visa sponsorship tier 2 general for 3-4 months period between the current visa expiry and my eligibility to apply for ILR ?

My question is that can I apply for ilr in September 2020 ?

No as you don't qualify as it is not within 28 days before reaching the 5byear mark on tier 2.

Or do I need another visa sponsorship tier 2 general for 3-4 months period between the current visa expiry and my eligibility to apply for ILR ?

Yes.