So if you have an HDHP through work and your employer is paying you back before you meet the deductible, you may NOT be qualified to contribute to a health savings account (HSA). 

Now that pretty much smells like skunk but here's the deal. There are some things that your employer may be able to pay for like preventative care or what is called "disregarded coverage" (things your health plan wouldn't pay for anyway). 

Of course it's ok for your employer to contribute to your HSA and you can pay for those expenses under the deductible with those funds, but when they start reimbursing you outside of the HSA, that's when things get squirrely.

For sure, if you have a high deductible health plan (HDHP), by all means, you want to be sure you are able to have an HSA too.  If you have any questions about things that might disqualify you from being able to open or contribute to an HSA be sure to consult with a good insurance agent or your company's benefits department.