The highly sought-after free-agent winger told reporters Monday that he still needs to mull over the offers on the table.
"The goal is to make the most informed decision I can," Parise told reporters outside of his agent's office in Mississauga, Ont. "I'm not putting a deadline on anything. It's such a long-term, important decision you have to make sure you look at everything."
Parise scored 31 goals and 38 assists in 82 games in 2011-12, second on the New Jersey Devils in goals and third in points.
Since being selected by the Devils 17th overall in the 2003 NHL Draft, Parise has notched 194 goals and 410 points in 502 games. He set career highs in 2008-09 with 45 goals and 94 points.
Parise received some criticism for not being a dominant player for much of New Jersey's recent run to the Stanley Cup final, finishing with eight goals and seven assists in 24 playoff games, with a minus-8 rating. In the six games against Los Angeles, he finished with a goal and a minus-5 rating.
The Minneapolis native missed most of the 2010-11 season due to a knee injury, appearing in just 13 games. But in his other six NHL campaigns, he's been absent a total of just three games.
Ryan Suter is unquestionably the biggest prize on the market when it comes to defencemen.
Agent Neil Sheehy told Joshua Cooper of the Tennessean on Monday evening that it will be at least one more day until an official announcement of note.
"There will be no decision tonight out of Ryan and there’s no timetable for his contract signing at this time," Sheehy said.
Since 2005-06, Suter has played in 542 NHL games with the Nashville Predators, scoring 38 goals and 200 assists, along with 396 penalty minutes.
Suter's decision could affect Nashville's ability to retain their top defenceman, Shea Weber. Weber, the two-time Norris Trophy finalist for top NHL defenceman, is a restricted free agent.