ST. PAUL — Ramsey County leaders upped their offer Thursday to be the home of a new Minnesota Vikings stadium to a total of $375 million, while the city of Minneapolis offered $313 million for the team to rebuild at the current Metrodome site.

The two local governments submitted dueling proposals Thursday to Gov. Mark Dayton as each seek to host a new stadium. Ramsey County board members want to build in suburban Arden Hills, north of St. Paul, while Minneapolis Mayor R.T. Rybak is trying to keep the team in his city’s downtown.

Dayton, who supports the team’s push for a public subsidy to replace the Metrodome, had set Thursday as the deadline for the proposals as he and lawmakers look to vote on a package in the upcoming legislative session.

Ramsey County leaders said they could raise $24 million a year with the addition of a 3 percent sales tax on food and liquor. The Minneapolis plan calls for raising $6.5 million a year for 30 years, plus $150 million for construction, from sales taxes already in place.

Vikings Vice President Lester Bagley said Thursday that the team continues to prefer the Arden Hills deal, but did not close the door on Minneapolis and said ultimately the team would build wherever the Legislature decides.