Quoting Latvian Foreign Ministry spokesman Karlis Eihenbaums, it was reported that "technical issues" had so far prevented the passport being handed over to Greste, who also possesses Australian citizenship.
One option could be to send a mobile passport mission to the prison, where Greste is being held in Cairo, while another might be to use intermediaries to deliver a ready-made passport to Greste.
"It is clear that this is not happening quickly. We have consulted with colleagues in Australia," said Eihenbaums, as both countries work in tandem to try to secure Greste's release.
Greste's case has become an international cause celebre after he was sentenced earlier this year to seven years in prison after being convicted of a variety of charges including supporting a terrorist organization, broadcasting false information and filming without a permit.
Journalists' groups have denounced the conviction and the entire judicial process in Egypt was viewed by many commentators as farcical.
Several of Greste's Al Jazeera colleagues also received lengthy prison sentences.
Despite being born in Australia, Peter Greste qualifies for Latvian citizenship via his father. Changes to citizenship laws introduced last year extended dual citizenship chances to nationals of a selection of countries including Australia and New Zealand.