According to The Daily Star, discussions have already taken place with both franchises regarding a potential deal.
However, Rana's participation in the BBL, which runs from December to January, will depend on receiving a No Objection Certificate (NOC) from the Bangladesh Cricket Board (BCB).
The BCB will have to consider the 22-year-old's workload and fitness, particularly with Bangladesh facing important Test series against West Indies, South Africa and England in the current World Test Championship cycle.
Rana recently recovered from a side strain that ruled him out of Bangladesh's two-Test series against Australia.
He has also been rested from the upcoming Asian Games squad and could return to competitive action during the Afghanistan series.