In a letter to team owner Lemieux, Balsillie said he is ready to begin negotiations right away and urged quick action to avoid a sale to another buyer who would automatically move the team to another city.
"Despite recent difficulties, I continue to be very interested in the team and in working towards an arena deal that is a benefit to the team and to the City of Pittsburgh," Balsillie said.
The head of BlackBerry maker Research in Motion invited Lemieux to go "arm and arm with me" to commissioner Gary Bettman to "make one last effort to get a deal done."
Balsillie, who abruptly pulled out of a US$175 million deal to buy the club last week, opened his letter with an apology to Lemieux, saying he regretted "that you have interpreted our inability to reach an agreement as an offence to you or the team.
"That was certainly never my intent and I apologize."
The letter was published Friday in the Pittsburgh Post-Gazette. Balsillie could not immediately be reached for comment.
Lemieux said Monday the Penguins were "shocked and offended" that Balsillie withdrew his offer.
The withdrawal came prior to a Pennsylvania gaming board vote that was to determine whether a new arena was built for the 40-year-old franchise.
Lemieux added that he would keep Balsillie's deposit and said that "the deal with Mr. Balsillie is dead."
The Penguins had another setback on Wednesday, when the gaming board voted unanimously to award Pittsburgh's slots machine license to PITG Gaming, rather than Isle of Capri Casinos.
Isle of Capri was committed to building a US$290 million arena next to a casino if it got the slots license. The new building would replace the 45-year-old Mellon Arena, the NHL's oldest rink.
After the vote, Lemieux announced that the Penguins were off the market and he would consider relocating the team to another city, although he would continue to seek other ways to have an arena built in Pittsburgh.
Balsillie pulled out of negotiations when the NHL insisted he agree in writing not to move the club even if the Isle of Capri arena deal fell through.
In his latest letter, Balsillie said he was ready to start negotiating Plan B.
"On our side all the papers have been signed and everything is in place to close our transaction immediately but for the NHL Consent Agreement," said Balsillie. "However, we must move quickly."
Plan B scenarios to finance a new rink are under discussions at various levels of government and with the winner in the slots license competition, Don Bardon.
The Penguins' lease at Mellon Arena expires in June, after which the team is free to leave.
Other cities interested in landing an NHL club include Kansas City, Las Vegas, Houston, Portland, Ore., and Winnipeg.