The country's cricket board said it would launch a probe after local media accused selector Atahar Ali Khan of taking commissions from the deal with national captain Habibul Bashar and star player Mohammad Ashraful.
"If it is found that the selector took commissions or in any way influenced the deal with the national cricketers, we will take action," cricket board chief executive officer Mahmudur Rahman told a press conference.
Khan, whose company Trendsetter Limited is the sole distributor of Reebok shoes and sportwear in the country, said the accusation was baseless.
"I did not know anything about the deal. Reebok International or Reebok India, from where my company brought goods, did not consult with me about the endorsement deal," he said.
Cricket has overtaken football as the most popular game in sports-mad Bangladesh after Test status was granted in November 2000.
Many of the national players have endorsement deals with local companies while some are popular faces in television commercials.
Cricket officials said they gave the go-ahead to the three-year deal in June after they found it did not clash with official sponsors.
Under the agreement, the cricketers would wear Reebok logos on their bats and also use the company's accessories.
But last week several newspapers alleged that Khan took huge commissions and raised "ethical" questions about his role as a selector.
Bangladesh captain Bashar, currently in Zimbabwe leading his team in a five match one-day series, admitted the deal was "lucrative" but he did not disclose details.
"What I can say is that it's a very lucrative deal and it would mean a lot to Bangladeshi cricketers," Bashar said, adding the deal would be effective from the Zimbabwe tour.
The cricket board said their investigations would also see Bashar and Asharful questioned about the allegations.
New York Stock Exchange-listed Reebok could not be immediately contacted for comment.