Detective Branch's Inspector Fazlur Rahman, who is in charge of the probe, pleaded for more time on Monday, when a Dhaka court fixed Apr 26 to submit the investigation report.
Court police's Sub Inspector Md Mozammel told bdnews24.com that the court has extended the deadline for the 24th time.
Roy and his wife Rafida Ahmed Bonya were attacked on the night of Feb 26, 2015 on the Dhaka University Campus.
Machete-wielding men attacked the couple as they came out of the Ekushey Book Fair.
Avijit suffered a deep gash on his head and died while Bonya survived but lost a finger in the assault.
His father Ajay Roy, a well-known physicist who has taught at the Dhaka University for a long time, started a police case over the incident.
Police said they have so far made seven arrests in the case and one of them Abul Bashar secured bail, according to court documents.
Sub Inspector Mozammel, however, said Bashar was in jail in another case until his death recently.
The other suspects in the case are Md Towhidur Rahman Gama, Shafiur Rahman Farabi, Sadek Ali Mitthi, Aminul Mallik, Julhas Biswas, Md Jafran Hasan and Manna Yahya alias Manna Rahi.