Unfortunately, no.
The IRS is very specific about the HDHP that is required in order to have an HSA.
"A high deductible plan (HDHP) can be combined with a health
savings account (HSA), allowing you to
pay for certain medical expenses with
money free from federal taxes. The IRS defines a high
deductible health plan as any plan
with a deductible of at least $1,350 for
an individual or $2,700 for a family." (Emphasis added.)
Source: https://www.healthcare.gov/glossary/high-deductible-health-plan/