His agent, Neil Sheehy, said he did not know whether Visnovsky will remain with the KHL's Slovan Bratislava, where he played during the lockout.
Visnovsky issued a statement through Sheehy last week expressing his desire to remain in Europe. The Islanders can suspend Visnovsky for failing to report.
The KHL and NHL have an agreement that all players with NHL contracts are obligated to return to the NHL once the lockout is lifted.
Visnovsky's case might be the first legitimate test of the sincerity of the agreement.
"The KHL has repeatedly said that they will not permit him to play, so I guess we will have to see what happens," deputy commissioner Bill Daly said when reached via email.
According to a statement released by the KHL translated into English, Visnovsky appealed to the league to enter into a contract with Slovan Bratislava for the rest of the 2013 season but had that plea denied.
However, the memorandum allows for negotiations between the KHL and NHL on the matter and it appears that option will be explored.
"[KHL] and representatives of the National Hockey League in the near future will begin joint consideration of the case Lubomir [Visnovsky] to identify the possibility of compromise," the statement said. "In the absence of a positive outcome of the negotiations the player and the club in accordance with the 'Memorandum of Understanding' will be able to exercise their right to appeal under the law through arbitration of the dispute."
According to International Ice Hockey Federation spokesperson Szymon Szemberg, the IIHF has not yet received an official letter of complaint from the NHL on the situation.
Should the league appeal to the IIHF, international hockey's governing body, that probably would be the next step.
The IIHF's involvement would likely only come should the NHL and KHL fail to resolve the situation on their own.
"Please keep in mind that even before IIHF regulations come into play, the NHL and the KHL have an independent memorandum of agreement drawn up specifically to avoid cases where each other contracts are not respected," Szemberg said when reached via email. "Bill Daly has repeatedly stated that he expects the KHL to respect their side of the agreement."