The right-arm fast bowler's decision is awaited, reports bdnews24.com.
"We have contacted Aaqib Javed. Our CEO Nizam Uddin Chowdhury told me we will get a 'yes' or 'no' answer by the day after tomorrow," Hassan said in a press conference on Sunday.
Former Zimbabwe allrounder Heath Streak, who had held the post since May 2014, revealed his decision not to extend his contract with the BCB via email towards the end of last month.
BCB's cricket operations committee chairman Akram Khan had earlier said they had set their sights on four bowlers - Sri Lanka's Champaka Ramanayake and Chaminda Vaas, Aaqib Javed and India's Venkatesh Prasad.
The BCB has a backup plan if Javed turns down the offer.
Javed ended a successful term at the United Arab Emirates in April.
He may take up the post of director of cricket at Lahore Qalandars but this is yet to be confirmed.