You can do a rollover or even better a trustee-to-trustee transfer. In a rollover the check goes through you, and you have 60 days and you can only do one per year. Contact the new company for help.
According to the IRS:
Generally, a rollover is a tax-free distribution to the taxpayer of
cash or other assets from one HSA that the taxpayer contributes to
another HSA. The contribution to the second HSA is called a rollover
contribution; these contributions:
- Are not included in taxpayers' income
- Are not deductible
- Do not reduce taxpayers' contribution limit
Taxpayers can also roll over amounts from Archer MSAs into an HSA.
They do not have to be eligible individuals to make a rollover
contribution from their existing HSA to a new HSA.
Rollovers are not subject to annual contribution limits and a rollover
contribution is not always cash; for example, it could be a
Certificate of Deposit (CD). The taxpayer must roll over the amount
within 60 days after the date of receipt, and may only make one
rollover contribution to an HSA during a one-year period.
See Publication 969 for more information on rollover contributions.
If the taxpayers have their HSA funds transferred directly into
another HSA in a trustee-to-trustee transfer, this is not considered a
rollover. There is no limit on the number of these transfers. Do not
include the amount transferred in income, deduct it as a contribution
or include it as a distribution on Form 8889.
There are several issues though.
- Your company might only put money in their preferred provider which means you may have to do periodic transfers during the year. Thus the trustee-to-trustee transfer is better.
- You could skip having the money pulled directly from your paycheck and make periodic contributions from your bank. But that would mean the funds are taxed for Social Security and FICA.
- In some (many?) cases the employer pays some or all of the monthly cost of the account, if you pick your own trustee you may have a monthly fee, which can dwarf the small amount of interest being earned.