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/