Inclusion Criteria:

* Subjects must be at least 18 years of age at the time of signing the Informed Consent Form (ICF); must voluntarily sign an ICF; and be able to meet all study requirements
* Morphologically confirmed diagnosis of AML or MDS in accordance with World Health Organization (WHO) diagnostic criteria
* Subjects with relapsed/refractory AML who are refractory or relapsed to all conventional therapy and do not have any FDA approved or standard therapeutic options \& subjects with intermediated/high/very high IPSS-R MDS who are refractory or relapsed to at least 6 cycles of hypomethylating agent based therapy (azacitidine / decitabine based)
* WBC must be \<25,000 and may be reduced with hydroxyurea to reach this goal prior to study start
* A post-consent bone marrow biopsy must be performed and tissue collected for correlative analysis for entrance to this trial. Correlative sample collection will not be optional on this study.
* Subjects must have an Eastern Cooperative Oncology Group (ECOG) Performance Status of 0-2
* Recovery to ≤ Grade 1 or baseline for any toxicities considered to be due to prior systemic treatments, excluding alopecia
* Must have adequate hepatic and renal function as follows:

ALT (SGPT) and/or AST (SGOT) ≤ 3x upper limit of normal (ULN) or ≤ 5x ULN if considered to be leukemia related; Direct bilirubin ≤ 1.5 x ULN or ≤ 3x ULN (in patients with know Gilberts syndrome or if considered to be leukemia related)

* Serum creatinine clearance ≥ 60 mL/min/1.73 m2 either measured or calculated using standard Cockroft-Gault formula

Exclusion Criteria:

* Acute Promyelocytic Leukemia
* Low or very low risk MDS by IPSS-R after failure/progression of first line therapy with hypomethylating agents
* Active, uncontrolled infection. Patients with infection under active treatment and controlled with antibiotics are eligible. Use of prophylactic anti-microbials per institutional standards is allowed.
* Active documented central nervous system (CNS) leukemia. Patients with a known history of CNS leukemia will be eligible if they have at least two most recent consecutive LPs showing clearance of CNS disease and no active/progressive symptoms thought to be related to the CNS disease.
* Concurrent treatment with a non-permitted concomitant medication (as noted in protocol appendix)
* Concurrent anticancer treatment, major surgery, or the use of any investigational drug within 14 days before the start of trial treatment
* Other malignancy currently being treated or likely to need treatment in next 6 months with the exception of basal or squamous cell carcinoma of the skin or cervical carcinoma in situ, surgically removed malignancies or malignancies definitively treated with chemotherapy, XRT and/or surgery with no evidence of active malignancy or not anticipated to need treatment in next 6 months or malignancies on maintenance therapy (e.g. tamoxifen for breast cancer) will be allowed after discussion and approval by both MPIs
* Pregnant or breastfeeding females
* Known current alcohol or drug abuse
* Clinically significant cardiovascular disease within the past 6 months (e.g. percutaneous intervention, coronary artery bypass graft, documented NYHA class III/IV cardiac heart failure, unstable angina or MI, poorly controlled atrial or ventricular arrhythmia) as determined by the investigator
* Any psychiatric condition that would prohibit the understanding or rendering of informed consent
* Legal incapacity or limited legal capacity to sign consent and/or participate in the trial
* Any condition deemed by the investigator to make the patient a poor candidate for clinical trial and/or treatment with investigational agents.
* Previous exposure to the investigational agent (danvatirsen) or to other STAT3 inhibitors