No official confirmation has been given, but the Canadian Manufacturers and Exporters group says the federal cabinet is expected to give approval later this week.
The Prime Minister's Office would not comment.
But reports say a joint announcement could be made as early as Friday.
Michigan Gov. Rick Snyder said last month he was looking at an "interlocal" agreement with Canada, which would not require approval from the state legislature.
His spokeswoman, Sara Wurfel, said she cannot confirm any announcement or agreement at this point.
However, she added, "the governor...reiterated today that this is one of the top priorities for him to get done because of the importance to Michigan's economy...and what it means for job creation, international trade, export and the leveraging that Michigan can gain for helping address its roads and bridges."
CME policy head Mathew Wilson says a new crossing is critical to Canada's economic competitiveness and job growth.
About one-quarter of all Canada-U.S. trade currently flows across the privately-owned Ambassador Bridge between Windsor and Detroit, which has long been a major choke point for cross-border traffic.
The owner opposes a new bridge, but Windsor West MP, New Democrat Brian Masse, says it will be good for the economy, the environment and for Windsor.
"There's around 24 international bridges and tunnels between Canada and the United States," Masse said Tuesday in Ottawa.
"All the other ones except for one are publicly owned, so what we've had over the years are high toll rates (and) questionable practices."
Massse said another bridge and a new highway system connecting to it would lead to less idling by trucks, which will be better for the environment.