Citing league and team sources, the Tribune-Review claims the Penguins' offer to Parise was the largest for a UFA in team history.
The New Jersey Devils, Parise's current/former team, also pitched an offer, as did the Carolina Hurricanes, Dallas Stars, Philadelphia Flyers, Detroit Red Wings, Los Angeles Kings, Minnesota Wild, Winnipeg Jets and several other clubs.
The Hurricanes and Stars have already been told Parise will not accept their offers.
It's unclear what the Penguins offered, though it's believed to be in the 10-year range worth around $8 million per season.
The Tribune-Review reports that both Sidney Crosby and Paul Martin each spoke with Parise, who is good friends with both players.
Parise is expected to make his decision later today.
Meanwhile, the Penguins are also in the market for a defenseman and have inquired about both Ryan Suter and Matt Carle.