Investigator are suspecting that the couple are members of Jama'atul Mujahideen Bangladesh (JMB) and are trying to arrest that couple at present.
Sources from the investigation said a person named Karim had rented an apartment in Bashundhara residential area where he supposedly resided with his wife and two children.
But within two days of the Gulshan attack, the couple fled the apartment.
Investigators say that they have intelligence that the couple rented multiple apartments in the city.
However, investigators confessed they do not know the couple's whereabouts.
Another investigation source said that police had raided three apartments known to be rented by Karim.
They were all unoccupied. The landlords said the family left without any prior notice.
The Police raid revealed that the apartments where sparsely furnished with mattresses on the floor and just a few pots and pans to cook with.
No documents related to the Gulshan attack or future attacks where found, the source said.
The Gulshan attack case is at present being investigated by Dhaka Metropolitan Police (DMP)'s Counter Terrorism and Transnational Crime (CTTC) unit. Other law enforcing agencies – RAB, detective police and several other intelligence agencies are assisting with the investigation.
CTTC Chief Additional Commissioner Monirul Islam said they were also suspecting a Bangladeshi born Canadian citizen Tamim Ahmed Chowdhury to be deeply involved in the planning of the Gulshan attack.
Tamim is known to be one of the top leaders of the recently activate fraction of JMB. He is currently working to promote a new JMB, the CTTC chief said.
Tamim returned to Dhaka in 2013
The militants who were involved in the Gulshan and Sholakia attacks were taken to Jhenaidah and Gaibandha for combat training.
They were then divided into two groups that carried out the Gulshan and Sholakia attacks respectively.
Inspector General Of Police AKM Shahidul Haque had earlier said that they had received information about some of the criminals behind the attack and were looking for them.
However, investigators have only arrested four people in connection including two landlords who failed to file information about their tenants.
Their tenants later turned out to be militants.
One of the landlords arrested was the acting Pro VC of North South University.
It has been a month since the two militant attacks in the country and Investigation sources said they have information about some nine new people including the planner of the Gulshan attack but no arrests have been made in connection.
During the Kallyanpur raid on July 26 where police killed nine militants, investigators said they found evidence that the Kallyanpur militants were linked with the Gulshan attackers and that they were planning an even bigger attack.
Acting Deputy Commissioner of CTTC Saiful Islam said they were conducting the investigation keeping every minute detail in mind.