Parise tore the meniscus in his right knee in a game Oct. 30 against the Los Angeles Kings. He underwent arthroscopic surgery Nov. 2.
"He will play this season, unless there is something unforeseen that happens," Lamoriello said, according to the newspaper.
Parise has three goals and three assists in 12 games with New Jersey, which likely will miss the playoffs for the first time since 1995-96, despite a monumental surge since Jacques Lemaire took over as coach in mid-December after John MacLean was fired.
Parise practiced with the full team at AmeriHealth Pavilion in Newark on Thursday, according to The Star-Ledger. He had been practicing on his own since March 4. He has been cleared to by his surgeon to have contact in practice. The original hope was that he'd be back skating in early February.
Lamoriello wouldn't give an exact date for his return, but told reporters March 3 that it would take at least two to three weeks before a date could be established.
"He's on a time frame, let's put it that way," Lamoriello told the newspaper.
The Devils (34-35-4) have just nine games remaining. The play the Penguins in Pittsburgh Friday and the Sabres in Buffalo Saturday. Parise said he will travel with the team but will not play Friday and is doubtful for Saturday as he gets back into game shape.
Parise, who led the team in points the previous two seasons, is a restricted free agent at the end of the season.
Mike Mazzeo is a regular contributor to ESPNNewYork.com.