Curious George, the lovably troublesome monkey of H.A. Rey’s children’s book series, could be one step closer to eviction this week.

The World’s Only Curious George Store, prominently housed at 1 John F. Kennedy St. in the heart of Harvard Square, is part of a planned redevelopment by New York real estate firm Equity One, which bought the building and its neighbors for $85 million in October. The company will appear before the Cambridge Historical Commission Thursday evening to seek its approval for the project, a key hurdle in finalizing the space’s redesign.

Collectively dubbed “The Harvard Collection,’’ the project would convert the property, which also includes 2-7 and 9-11 JFK St. and 18-20 Brattle St., into a shopping mall, adding two stories and a glass-walled “roof top pavilion,’’ according to plans Equity One filed with the commission in August.

Equity One representatives failed to return repeated calls.

The space now occupied by the Curious George Store, with its bright yellow and red facade, is adjacent to the Harvard Square T stop. It will house an entrance, elevator, and stairway, according to a proposed floor plan.

“If you’re going to spend that much money for these buildings, eventually soon there’s got to be a plan coming out to do something more with them,’’ said Adam Hirsch, who with his wife, Jamie, has owned the store for the past four of its total 21 years. “It’s not like this was a surprise.’’

Other current tenants include Urban Outfitters and Dewey, Cheetham and Howe, the company behind NPR’s “Car Talk,’’ all of whose impending fate has stoked the ire of many Cambridge residents who view the changes as yet another step in diluting the idiosyncratic character of the Square.

“There’s a huge amount of public interest that we’ve been getting, largely from people who were concerned about the stores,’’ said Charles Sullivan, executive director of the historical commission. “Most recently the Curious George Store had been generating a lot of e-mails.’’

Sullivan compared the response to that surrounding the Tasty Sandwich Shop, a former Harvard Square staple whose closure in 1997 prompted charges of gentrification and commercialization in the historic district. Despite the backlash, a CVS Pharmacy now sits where the Tasty once did.

“Community impact definitely has an impact,’’ Sullivan said. “Which way it might influence the committee’s decision [Thursday], I can’t predict.’’

If the proposal is approved by the commission, Sullivan said, it still will face other regulatory hurdles.

Though the Curious George Store, which sells books, toys, and other products linked to its namesake, has been scouting out new homes in the area, Hirsch said the bigger goal in the meantime is to remain committed to the people that made it a landmark to begin with.

“We’re a small mom-and-pop retailer,’’ he said. “We need to stay focused on our team, making sure they’re comfortable and happy, our merchandise, our customers, and making sure they know we’re here. We have no intentions to move at all until we have to, which is at least a year away.’’

Any grander plans will hinge on the outcome of the meeting Thursday night, which Hirsch plans to attend, if only to learn more about the project himself.

“I’m absolutely going to be there,’’ he said. “I think anyone who has a stake in the game or cares about Harvard Square should be there.’’

Joe Incollingo can be reached at joe.incollingo@globe.com