The answer is NO. You cannot be covered by a general purpose health FSA and make HSA contributions. Because your health FSA is active (available to you for payment of medical expenses) through the end of this calendar year, that makes you ineligible to contribute to a HSA this year.
"Interaction Between HSAs and Health FSAs
Section 223(a) allows a deduction for contributions to an HSA for an “eligible individual” for any month during the taxable year. An “eligible individual” is defined in § 223(c)(1)(A) and means, in general, with respect to any month, any individual who is covered under an HDHP on the first day of such month and is not, while covered under an HDHP, “covered under any health plan which is not a high-deductible health plan, and which provides coverage for any benefit which is covered under the high-deductible health plan.”
In addition to coverage under an HDHP, § 223(c)(1)(B) provides that an eligible individual may have disregarded coverage, including “permitted insurance” and “permitted coverage.” Section 223(c)(2)(C) also provides a safe harbor for the absence of a preventive care deductible. See Notice 2004-23, 2004-1 C.B. 725. Therefore, under § 223, an individual who is eligible to contribute to an HSA must be covered by a health plan that is an HDHP, and may also have permitted insurance, permitted coverage and preventive care, but no other coverage. A health FSA that reimburses all qualified § 213(d) medical expenses without other restrictions is a health plan that constitutes other coverage. Consequently, an individual who is covered by a health FSA that pays or reimburses all qualified medical expenses is not an eligible individual for purposes of making contributions to an HSA. This result is the same even if the individual is covered by a health FSA sponsored by a spouse’s employer.
However, as described in Rev. Rul. 2004-45, 2004-1 C.B. 971, an individual who is otherwise eligible for an HSA may be covered under specific types of health FSAs and remain eligible to contribute to an HSA. One arrangement is a limited-purpose health FSA, which pays or reimburses expenses only for preventive care and “permitted coverage” (e.g., dental care and vision care). Another HSA-compatible arrangement is a post-deductible health FSA, which pays or reimburses preventive care and for other qualified medical expenses only if incurred after the minimum annual deductible for the HDHP under § 223(c)(2)(A) is satisfied. This means that qualified medical expenses incurred before the HDHP deductible is satisfied may not be reimbursed by a post-deductible FSA even after the HDHP deductible has been satisfied. To summarize, an otherwise HSA eligible individual will remain eligible if covered under a limited-purpose health FSA or a post-deductible FSA, or a combination of both."
http://www.irs.gov/irb/2005-49_IRB/ar08.html#d0e1151
