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Scott G. Winterton, Deseret News
Utah's Paul Millsap holds his head after committing a foul as the Utah Jazz and the Los Angeles Lakers play in LA in Game 2 of the first round.

With the Jazz's efforts to trade Carlos Boozer or Andrei Kirilenko still apparently ongoing, negotiations between the franchise and backup power forward Paul Millsap press on as well.

"I know (general manager) Kevin O'Connor is continuing to have dialogue with Paul and Paul's agent," Jazz president Randy Rigby said Tuesday, "and I know we're continuing to express an interest on our part to have Paul a part of our team.

"It's then just a matter," Rigby added, "of coming to an agreement."

The NBA's weeklong summer negotiating period came to a close at 10 p.m. Tuesday, allowing the league's unrestricted free agents to sign new contracts and its restricted free agents — including Millsap — to either sign another team's offer sheet or re-sign with his own team.

Even if Millsap did sign another club's offer sheet, the Jazz have the right to match it — and Rigby suggested doing so still is the franchise's plan.

But, Rigby also indicated, there is a limit as to just how much Utah is willing to pay its 2006 second-round draft choice.

He did not say what that ceiling is.

"We've invited and encouraged them (Millsap's representatives) to look at the market and do what they feel like they need to do," he said, "and we're doing what we think is best for us, which is coming up with what we feel is a fair value for Paul and ourselves.

"We feel strong," Rigby added, "about what our position is."

Millsap's camp initially was seeking a multiyear deal starting at $10 million or more, but there were no known takers when the negotiating period opened and no known offers as of Tuesday night.

That leaves a few possibilities, including accepting the Jazz's $1.03 million qualifying offer for next season and becoming an unrestricted free agent when many teams have more money in 2010, playing for midlevel exception money (a multiyear starting at $5.854 million) or accepting an offer from the Jazz that perhaps would start in the $6 million range.

The Jazz's ability to pay much more than that, however, was adversely impacted by decisions last week from Boozer, starting center Mehmet Okur and backup shooting guard Kyle Korver to opt in for the final year of their current contracts.

That pushed the Jazz's payroll for next season, not including Millsap and a requisite 13th player, to more than $73 million — and seemingly spurred efforts to trade starting power forward Boozer and/or small forward Kirilenko.

It also evidently put firmer parameters on just how far the franchise is willing to go to make good on its promise to match any offer sheet Millsap signs with another team.

"There's no question that it added more of a pressure on us of with regard to the degree of comfort that we have," Rigby said. "But I think we have to — particularly in today's economic environment, and this behooves every team, and us in particular — assess what all these players, and their value, is worth to us.

"Kevin (O'Connor) has done a masterful job of addressing that with each one of the agents."

The Jazz, Rigby suggested, have made it known they don't have buckets of money available for the taking.

"I think we have to now be very fiscally responsible ... as to how we're allocating our dollars to our players," he said.

E-MAIL: tbuckley@desnews.com