Parenteau, 33, played two seasons for New York from 2010-12. He had 53 points in 2010-11 and 67 in 2011-12, his only NHL seasons above 50, playing at times with Islanders center John Tavares.
"I got a chance to play with him my first year when [coach Jack Capuano] took over and we had a good thing going," Parenteau told Newsday. "I'm not assuming I will play there again, but if I do it will be awesome. He's one of the best in the League, the best on some nights. It's a big reason why I decided to come back."
Parenteau's 20 goals last season matched his NHL career high, set in 2010-11 with the Islanders, and led the Toronto Maple Leafs. His 41 points were second on Toronto to Nazem Kadri's 45 and the most he's had since 43 (in 48 games) with the Colorado Avalanche in 2012-13.
"I had a rough couple years, in Montreal especially, but I bounced back last year," Parenteau said. "I thought I might come back [to the Islanders] at the Trade Deadline last season but it didn't happen. I always thought I'd be back to Long Island."
Part of Parenteau's increased production stemmed from the fact he got top-six and power-play time because of the Maple Leafs' roster. He is looking forward to joining the Islanders, who won a Stanley Cup Playoff series last season for the first time since 1993.
"This team is more than a playoff team," Parenteau said. "They've been real legit the last couple years. There was no Johnny Boychuk, no Nick Leddy (on defense) when I was there; with them and Travis [Hamonic], not many teams have a top-three [defensemen] like that. It's a big reason why I decided to sign."
