BRUSSELS—Luxottica and Essilor have not offered any concessions to allay EU antitrust authorities’ concerns over their proposed €47 billion ($56 billion) merger, which could increase the likelihood that EU investigators will take a deeper look at the deal, Reuters reported on Wednesday.

The two companies had until Sept. 19 to offer concessions after the head of the bloc’s competition watchdog expressed reservations about the deal earlier this month.

The European Commission recognizes if the parties to a merger have made concessions. However, the filing on its website shows that Luxottica and Essilor had not done so.

Unless they managed to appease the Commission at last week's meeting, it is likely that the regulator will open a full-scale investigation lasting about four months following a preliminary review that ends on Sept. 26, according to Reuters. Some companies prefer to offer concessions during this phase after getting a better idea of the regulator's concerns.

Both Luxottica and Essilor declined to comment on the EU enforcer's concerns. U.S. regulators are also examining the deal, which was approved by New Zealand authorities earlier this month.