Councilwoman Robin Kniech, the bill's sponsor, amended it in recent days to reduce the number of grow houses, in an effort to win support from fellow Councilman Kevin Flynn.
"We have a saturated city," Flynn said at last week's meeting that went past midnight.
The Denver Post reports Flynn said he will probably vote for the bill Monday.
The measure would institute a ban on new marijuana dispensaries and grow houses, something the city already has in place on a temporary basis. It would also place more limits on where the businesses could be located.
If Council passes the bill Monday, it will go up for a final vote next month.