The extension comes after Shimachu last week accepted a higher bid from furniture chain Nitori Holdings Co Ltd and rejected an earlier agreed offer from DCM Holdings.
DCM has offered Shimachu shareholders 4,200 yen per share, valuing the deal at 164 billion yen ($1.57 billion), while Nitori has offered 5,500 yen per share in a 214 billion yen deal.
DCM has not raised its offer price.
Shimachu shares closed at 5,490 yen on Monday.
($1 = 104.4100 yen)
(Reporting by Daniel Leussink and Junko Fujita; editing by Jason Neely)