The animal-rights group People for the Ethical Treatment of Animals is offering to buy the anti-meat ad featuring "Lettuce Lady," who appears to be holding a hot dog -- but it's actually a veggie dog -- and the ad would be prominently displayed at the Middleton museum, the Wisconsin State Journal reported.
The ad would help the financially struggling museum, given more time last week to pay off a $200,000 county loan.
Barry Levenson, the museum's founder and curator, said he's considering the ad.
Ingrid Newkirk, PETA's president, said PETA also could provide the museum veggie dogs or cocktail-size samples to hand out.
"While your whimsical displays and mouth-watering condiment samples add to a perfect family outing, we hate to see that delicious mustard slathered on waist-expanding, artery-clogging meat," Newkirk wrote in a letter to Levenson.
The museum, which features a collection of more than 5,300 mustards as well as mustard-related exhibits, sells hot dogs and brats in its gift shop and could sell veggie dogs as well, the Journal said.
Levenson said he doesn't think PETA is asking him to stop selling meat.
"We don't want to offend anyone, but I look at it as something belonging in the museum," he said.
"A lot of people think of mustard as for hot dogs and don't think of mustard as something to go with vegetables. And one of the parts of our mission is to educate people as to the many uses of mustard. I don't think that requires us to take sides."