OAKLAND — The lunchtime line was long Tuesday at Genova Delicatessen in North Oakland, but life in the Temescal neighborhood it has called home for nearly a century could soon end.

Deli co-owner David Devincenzi said Tuesday the shop at Temescal Plaza at 51st Street and Telegraph Avenue could close by May 1 if they cannot agree on rent with the landlord.

“He keeps telling me rents are going up, but doesn’t our business have anything to do with it? If we weren’t in this plaza, the whole plaza would sink,” Devincenzi said. “They are living on another planet.”

A representative for Rudd Properties, which owns the plaza along with Reininga Corp., declined an interview. But the company said in a statement it plans to continue negotiating with Devincenzi.

The deli has operated in Temescal since 1926, and has survived a lot — the construction in the 1960s of the Grove-Shafter Freeway that divided the neighborhood, damage from the 1989 Loma Prieta earthquake, and Temescal’s emergence as a premier shopping and dining district in Oakland.

Along with the Colombo Club on Claremont Avenue, Genova Deli is one of the last holdovers from when Temescal was an Italian enclave. It moved to its current location in the mid-1990s, where it shares a parking lot with Walgreen’s, Round Table Pizza, a post office and other stores.

“It’s been there forever,” said Harry Yaglijian, whose family opened the Original Kasper’s Hot Dogs on Telegraph and 45th Street in 1943. “The beauty of the original Genova store is it just smelled great. You walked in there, there’d be barrels of pasta, they’d have bins of rolls, salami hanging from meat racks. And the current place is great. Where else are you going to get sandwiches like that?

However, Devincenzi said rents have become too expensive to operate his store, where about 25 employees make sandwiches daily. He said he regrets not purchasing property with his father in Temescal; he owns the property at his Napa location and the deli’s ravioli factory on Broadway across from Oakland Technical High School.

“Everything is wide open,” he said. “Unfortunately, that’s just the way it is.”

At lunchtime Tuesday, Oakland resident Charity Pritchard was among 30 customers holding deli counter tickets and waiting for a sandwich. She said she would be “very sad” if the Genova closed.

“The people are great, the food is great — they make the best sandwiches,” Pritchard said.

“Despite that it’s slow, the food is just so good. I don’t think you can beat this sandwich,” 25-year-old Daniel McBride said of his Black Forest ham on sourdough.

Devincenzi said he hopes to have a deal worked out with the landlord before the lease expires at the end of May. If that fails, he may move the deli to another location, possibly the ravioli factory on Broadway. The deli’s website encourages customers to stock up on the company’s frozen products in case they have to close.

“In case something turns unfavorable, you’ll have it in your freezer,” Devincenzi’s wife, Patty, said Tuesday.

David DeBolt covers breaking news. Contact him in Oakland at 510-208-6453. Follow him at Twitter.com/daviddebolt.