DCM's tender offer, which values Shimachu at 164 billion yen ($1.6 billion) is due to run until Nov. 16 and has the support of Shimachu's management.
Nitori's possible bid could become another test case for Japan's corporate governance, which has been improving as boards come under pressure to give investors higher returns.
Placing a bid without consent from a target has been a long taboo in Japanese corporate culture but in recent years the number of such bids has been on the rise and welcomed as investors tend to support higher bids.
A hostile bid by a travel agent H.I.S. Co to buy hotel operator Unizo Holdings last year was a typical example.
Though the H.I.S. bid eventually failed, it prompted global foreign investment groups to place competing bids, helping the shares surge.
Already an activist fund has emerged as a shareholder in Shimachu. A government filing on Wednesday shows that an investment fund associated with prominent investor Yoshiaki Murakami has boosted its stake in Shimachu to 8.38%.
News of the possible bid by Nitori sent shares in Shimachu surging more than 13% to 4,760 yen in early trade, well above DCM's offer price of 4,200 yen and valuing the company at 185.4 billion yen.
Shimachu said it had not received a proposal from Nitori.
A DCM spokesman said the company would continue with its tender offer as planned, declining to comment on Nitori's announcement. DCM's shares plunged 8.2%.
A bid by Nitori, which sells a range of products from furniture to kitchen tools at affordable prices, highlights efforts by retailers to grow as the coronavirus pandemic slows consumption.
"We are considering possibilities for growth through mergers and acquisitions, including Shimachu," Nitori said in a statement.
Nitori's shares dropped 0.9% while the wider market edged 0.4% higher.
($1 = 105.3800 yen)
(Reporting by Chang-Ran Kim and Junko Fujita; Editing by Edwina Gibbs, Kim Coghill and Gerry Doyle)