The Senate takes up the plan after the state House approved it, 73-58, late Monday after 8 1/2 hours of debate, the Duluth (Minn.) News Tribune reported.
The newspaper said numerous senators, particularly Republicans, have expressed opposition to the plan and Senate Republican spokesman Steve Sviggum said the debate would likely be long and predicted a close vote.
Republican senators met behind closed doors for hours before the floor debate began Tuesday afternoon.
If it is approved, a House and Senate conference committee would work out details from two versions of the plan and the measure could reach Gov. Mark Dayton by late this week.
A House amendment would increase the amount the Vikings would pay from $427 million to $532 million, which team officials oppose.
"It's clear the Vikings are going to have to agree to more" funds than originally planned, Republican state Rep. Morrie Lanning said.
The state's contribution would be financed by gambling dollars from pull-tab devices and bingo.
Supporters of the new stadium say the Vikings could leave Minnesota if no stadium deal is reached.