Letang, 26, has one-year remaining on his current contract, which pays him $3.5 million. He is scheduled to become an unrestricted free agent next summer.
LeBrun also reported that Letang's camp countered the Penguins' offer with a long-term deal worth between $7.5 million and $8 million per season, but that deal was later rejected by Pittsburgh.
Discussions between the two sides are expected to continue, at some point, but it's unclear where negotiations will go from this point.
The Penguins have not yet officially entertained trade calls for Letang, but that could change this weekend. If Penguins GM Ray Shero decides to actively shop the Norris Trophy finalist, he'll likely attract the interest of all his 29 counterparts.
Alternatively, the Penguins could opt to hold off on contract talks until the NHL Draft concludes and wait until after the free agency market cools down in mid-to-late July, but that seems unrealistic and too risky for Pittsburgh, as the price tag for Letang could drop.
Letang does not own a no-trade or no-movement clause and could be dealt to any team that comes in with the best offer.
In 35 games with the Penguins this past season, the Montreal native registered five goals and 33 assists for 38 points, including a plus-16 rating.
Letang wants a no-movement clause included in his next contract.