In exchange, he was told, he would be paid 15 to 20 per cent of the earnings from the spot-betting.
BCB officials said Mortaza had been asked to reveal the name of the player who made the approach.
"This is a very serious offence," BCB spokesman Jalal Yunus said. "We have zero tolerance towards these things and will do whatever is needed to nail it down quickly. Mortaza has to disclose the name of the player."
Mortaza will speak to officials of the International Cricket Council's Anti-Corruption Security Unit before the matches start, Yunus said.
The six-team league is to be played in Dhaka and Chittagong, with the final on February 29.
Pakistan's Shahid Afridi, the most expensive foreign player at last month's auction after being sold to the Dhaka Gladiators franchise for US$700,000 (A$651,000), is not taking part because of international commitments.
Pakistan begin a one-day series against England in the United Arab Emirates this week.
- AAP