Cricket South Africa is considering a request from the Bangladesh board president Mustafa Kamal for South Africa to play Bangladesh in May.
Kamal made a request to CSA president Willie Basson last week and offered to pay all the costs, whether the series takes place in Bangladesh or South Africa.
CSA officials will meet with the South African Cricketers' Association and national coach Gary Kirsten next week to discuss the possibility of playing the series.
He said the decision will be based on South Africa's schedule and whether this fixture can be included without causing fatigue.
Bangladesh has no international cricket scheduled before the World Twenty20 in September.
Their trip to Pakistan, for an ODI and a T20 later this month, was put on hold after a court order placed a four-week embargo on the tour, and their visit to Zimbabwe in August was postponed because of work being done on the pitches in Harare and Bulawayo.