During the lockout, Visnovsky played for HC Slovan Bratislava, his hometown team, in the KHL. He expressed interest in playing in Slovakia for the remainder of the season.
However, the KHL is honoring NHL contracts and has not allowed Visnovsky to participate since the end of the lockout.
Nonetheless, Visnovsky has yet to return to North America.
"Lubo has personal reasons for not reporting to the Islanders right now, all of which have absolutely nothing to do with the New York Islanders," Visnovsky's agent Neil Sheehy told The Associated Press. "We will have to see how this situation plays out."
The Islanders also announced Friday that they have claimed defenseman Brian Strait off waivers from the Pittsburgh Penguins.
Strait, 25, has played in 12 games with Pittsburgh, with one assist and four penalty minutes.