The Daily Mail reports the banning of shirt sponsors is one of many proposals to be included in a white paper to be published before the end of the year.
The prohibiting of other forms of gambling at football grounds, such as advertising hoardings, is being considered but is understood to be far less likely.
Both halves of the Old Firm currently have sponsorship deals in place with betting companies. Celtic are backed by south-eastern Asian company Dafabet, while Rangers display both Red32 and Unibet on the front of their shirts.
Celtic have a contract in place until 2025, while Rangers agreed a new “multi-year” deal last season.
Those are the only two clubs in Scotland with betting companies as their front-of-shirt sponsor.