Visnovsky has been playing in Russia's KHL, but is required to return now that the lockout is over. The Islanders' season opens Saturday night at home against the New Jersey Devils.
Visnovsky, acquired in June from Anaheim, attempted to have the trade overruled but an arbitrator ruled in December that the deal was valid.
"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, wrote in an email to The Associated Press on Monday. "We will have to see how this situation plays out."
The KHL is complying with an agreement with the NHL and won't let Visnovsky play in Russia now that the lockout has ended.
Visnovsky scored six goals and had 27 points - 10 on the power play - in 68 games with the Ducks last season.
In 771 games over 11 NHL seasons with Los Angeles, Edmonton and Anaheim, Visnovsky has 117 goals and 450 points. He was an All-Star in 2007.
Strait has played in 12 NHL games with the Penguins, notching one assist and four penalty minutes.
Pittsburgh chose him with the 65th pick (third round) of the 2006 draft, but the 25-year-old native of Boston has spent most of his time in the minors. Strait has eight goals and 32 assists in 220 career AHL games with the Wilkes-Barre/Scranton Penguins.