Siam told reporters in Gaza city: "Contacts are underway with Palestinian groups who are trying to secure the release of the two journalists. Things are at an early stage, but they are encouraging."
Asked whether Palestinian security services had located the kidnappers, Siam said it was too "early" to say.
"That should remain secret in order to support the efforts and I hope that they will be released. There is reason to be encouraged," added the minister.
The minister was speaking one day before an ultimatum for the US to release all Muslim prisoners in its custody, set by their kidnappers, was to expire.
The US State Department rejected the demands, insisting the pair be released unconditionally, although US officials in the region have said they are working with Palestinian authorities to try to secure the men's release.
The so-called Holy Jihad Brigades demanded that all Muslim prisoners in the US be released within 72 hours, or Saturday at noon (0900 GMT); but did not say what would happen if the demands were not met.
The Hamas-led government, boycotted by the West, has repeatedly called for the two men to be released.