Kovalchuk, who turned 30 today, will miss his 10th straight game on Monday with a right shoulder injury. The Devils visit Air Canada Centre to face the Toronto Maple Leafs.
According to Devils coach Pete DeBoer, Kovalchuk had a good skating session on Sunday and will skate again on Monday in New Jersey.
"I would call him day-to-day," DeBoer told local reporters. "My conversation with [Kovalchuk] before we left New Jersey [Sunday] was he had a good day [Sunday] morning, he was going to try to have another good one [Monday] and we would talk tomorrow morning."