Property developer Liam Carroll has increased his stake in ferries group Irish Continental to 29.75%.
A statement to the stock exchange said his investment company had bought 772,000 shares yesterday.
If his stake reaches 29.9%, Mr Carroll would have to make a bid for the whole company.
Two groups - a management team called Aella and the Moonduster consortium - had been vying for control of the company, but the offer period involving the two came to an end on October 31 after a stalemate was reached. Moonduster involved One51 and Doyle Group.