"She's my soul mate. She's my love of my life," Benjamin Konkol told ABC News. "I feel she's still out there."
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Konkol said he is not a suspect and that he allowed police to search their home and voluntarily took and passed a lie detector test. He was the last person to see her when she was at home that morning. Konkol said he was at work when she went missing.
It's believed that Eller went for a jog in the Makawao Forest. Her car was found there the next day with her phone and wallet inside and her keys hidden under a tire. Friends say that this was her normal jogging routine.
Konkol said he and others believe she could be lost or injured in the forest.
"Not to rule out foul play -- there's always that possibility -- however, I feel strongly, and a lot of people feel strongly, that she's definitely in this forest," he said. "So I just want to encourage everyone to not give up hope."
Konkol said he and Eller have been dating for about a year.
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"Amanda is one of the most amazing people I know," he said. "She's radiantly beautiful -- driven, successful, intelligent, super kind, loving, just overall wants to live the best life she can live."
Konkol is among the dozens of volunteers and loved ones who have joined the search efforts, which have included dogs and drones.
"Hope is not lost," he said. "There's still so much of a chance that we can find her."
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ABC News contributed to this report.