The Security Council set the deadline in December in a resolution that threatened sanctions if Iran failed to comply.
Larijani and other Iranian officials have suggested that Iran place a formal limit on the degree of its enrichment as a guarantee that it is not developing an atomic weapon.
|"... justice necessitates that those who want to negotiate should halt their own nuclear fuel cycles"|
Mahmoud Ahmadinejad, Iranian president
ElBaradei has proposed that Iran suspend its nuclear work in return for a hold on UN sanctions.
In an interview in the Financial Times on Tuesday, ElBaradei said that the meeting with Larijani would be "a last-ditch effort to try to convince them [the Iranians] that it is in their interest to find a way to go into negotiations."
The meeting between Larijani and ElBaradei, their first this year, comes just over a week after Larijani met Javier Solana, the EU foreign policy chief.
The West fears that Iran wants to develop nuclear weapons but Tehran insists that its nuclear-enrichment programme is solely for power generation.
The Iranian president has ruled stopping uranium enrichment as a pre-condition to talks.
"We are in favour of dialogue. But in order for us to talk they are imposing a condition that would deprive us of our right," Ahmadinejad said during a rally in Gilan province on Tuesday.
"If they say that our nuclear production plant and its fuel cycle should be shut down, this is fine. But justice necessitates that those who want to negotiate should halt their own nuclear fuel cycles."