Banton will play first 8 league matches for Heat.
Steyn last featured in any game across formats in the IPL while playing for RCB.
Alex Hales has signed a one-year deal and will join Chris Morris as the second overseas player with the side.
Speaking ahead of his new journey, the legendary batsman said he is excited to play in the Big Bash League.
The new rule applies to the tied finals of BBL 2019-20.
It will be Mujeeb's second stint with the franchise after he got 12 wickets last season.
BBL is set to get underway on December 17.
If the Stars manage to sign the South African star, it would prove to be a huge marketing and business boost for the franchise.
Faheem Ashraf and Mohammad Hasnain also approached by Big Bash sides
Big Bash has been one of the most entertaining leagues and that's why it has completed 8 successful years.
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