The City Island Nautical Museum is in a whale of a fight – for bucks.

And it’s going up against some pretty big local cultural institutions to harpoon it.

The museum has been chosen as one of 40 cultural institutions in New York City to take part in an online contest for $3 million in grants to preserve historic landmarked buildings and sites, said museum vice-president Barbara Dolensek.

The Partners in Preservation contest is running now through Monday, May 21. People can vote for their favorite institutions by logging onto partnersinpreservation.com.

The group, making its first foray into New York City, is sponsored by American Express and the National Trust for Historic Places.

The City Island Nautical Museum, in existence since the 1960s, is housed in the landmarked former schoolhouse at 190 Fordham Street.

It hopes to use grant money to fix the staircase leading to the public entrance of the museum.

It is competing locally against the New York Botanical Garden, Bartow-Pell Mansion, Woodlawn Cemetery, and Mind-Builders Creative Arts Center in the borough, and large historical and cultural institutions around the city.

“This is a David vs. Goliath type of thing, because organizations like the Botanical Garden all have professional staff working on this competition, and even Bartow-Pell has a small, professional staff,” Dolensek said. “We have five volunteers, including four women named Barbara who are 70-years-old!”

Among 500 city organizations selected last year for possible inclusion in the Partners in Preservation competition, the museum was among 40 chosen in April after completing an application process and a survey, including writing a grant proposal, Dolenesk said.

“I was surprised that we were selected, because we were not well known,” Dolensek said. “But we certainly have a worthy project. The staircase is over 100-years-old and the bluestone is cracked, and we are urging people to use the ramp leading into the museum because the two sets of six stairs are in poor condition.”

Competing such institutions as the Guggenheim in Manhattan make it unlikely the Nautical Museum will place in the top four vote getters getting $1 million, Dolensek said, but at least all or some of the money needed to repair the staircase.

To help make itself more appealing to the committee making the final selection, the museum has beefed up its website cityislandmuseum.org and its Facebook page, which now has over 100 friends. It also held an open house on Saturday, May 5 and Sunday, May 6, Dolensek said.

Vote at partnersinpreservation.com, or find the organization on Facebook or through its mobile phone app.