A walkout would affect nearly 300,000 daily riders, creating a commuting nightmare in and around the nation's largest city.
Cuomo has so far appeared reluctant to insert himself into the dispute, but on Wednesday called for action by both sides.
"We must do everything we can to prevent Long Islanders from being held hostage by a strike that would damage the regional economy and be highly disruptive for commuters," he said.
Christopher Natale, general chairman of the Brotherhood of Railroad Signalmen Local 56, which represents some of the LIRR workers involved in the dispute, said he welcomed Cuomo's involvement and speculated the governor or someone from his office may join the negotiations.
"Not true," countered Cuomo spokesman Matt Wing.
Anthony Simon, the unions' chief negotiator, told The Associated Press in an email that they were returning to negotiations at the request of the governor and that they hadn't wanted to stop negotiating in the first place.
Both sides are seeking to settle a long-running contract dispute before this weekend; the unions have threatened a 12:01 a.m. strike Sunday if they do not get a deal.
Workers have been without a contract since 2010. President Barack Obama appointed two emergency boards to help resolve the dispute, but the MTA rejected both nonbinding recommendations. The emergency board's last proposal called for a 17 percent raise over six years while leaving work rules and pensions alone.
The MTA offered a 17 percent wage increase over seven years, but also wants pension and health care concessions, which both sides agree is the sticking point holding up an agreement.
The state comptroller, Thomas DiNapoli, has estimated a strike would be a "devastating blow" to a region that is still struggling to recover from Superstorm Sandy and the recession. He estimated economic losses of $50 million a day.