Redskins owner Daniel Snyder, left, and General Manager Bruce Allen, on the sideline before Washington played the Minnesota Vikings last October. (Ray K. Saunders/THE WASHINGTON POST)

With the NFL’s free agent negotiation period set to begin Saturday, and the signing period commencing at 4 p.m. the following Tuesday, the salary-cap strapped Washington Redskins enter a crucial week as they attempt to upgrade their roster and build on their first playoff appearance in five years.

The NFL notified its 32 teams Thursday night that the salary cap for the 2013 season is set at $123 million. For the Redskins, the figure is expected to be reduced by $18 million, the amount docked by the league as the second half of a two-year, $36 million penalty for how the team structured contracts during the uncapped 2010 season. After factoring in the penalty, Washington is believed to be $3 million over the cap.

Now that the team knows exactly where it stands financially, General Manager Bruce Allen and Eric Schaffer, the team’s vice president of football administration, have a fair amount of finagling to do. They have until March 12 to get below the cap for the start of free agency by either restructuring contracts or releasing players.

But the Redskins need to trim more than the $3 million required to get under the cap. They must create additional spending room to re-sign a number of their 19 players with expiring contracts as well as meet other needs through free agency. For example, in 2012 Washington’s re-signings of London Fletcher, Kory Lichtensteiger and Adam Carriker, and the free agent additions of Pierre Garcon, Josh Morgan, Brandon Meriweather, Madieu Williams and Tanard Jackson cost roughly $15 million toward the cap.

The only way Washington would be able to avoid slashing its roster and reworking numerous existing contracts would be if it pulled off the seemingly improbable quest of recouping some of that $18 million penalty for this year. Early last week, people with knowledge of the situation said Washington was considering seeking an injunction in an attempt to get some of that money back. But as of Friday evening, the team had not done so, those people said.

People around the league believe that even if the Redskins did opt to seek an injunction, their chances of winning aren’t very strong. Washington and the Dallas Cowboys — who were penalized $10 million against the cap over two years by the league — challenged the penalties in arbitration last year, but the case was dismissed. Twice a federal judge has rejected a claim by the NFL players’ union that NFL teams operated with a secret salary cap in 2010.

However, others believe the Redskins do have a chance, and that they have strong arguments that they are being penalized unfairly.

The Redskins could also use the threat of an injunction to try to negotiate a settlement with the league.

Redskins Coach Mike Shanahan declined an interview request last week, and earlier this month Allen declined to go into specifics on the team’s plans regarding their salary cap situation.

“There’s plenty of things we can do, but now is not the time,” Allen told reporters at the groundbreaking ceremony for the team’s new training camp site in Richmond.

Barring penalty relief, whose deals would the Redskins look to restructure?

Cornerback DeAngelo Hall has a salary cap figure of $8 million for 2013. He said at the end of last season that he was willing to do whatever it took to remain in Washington. The team could consider spreading that money out over two more years by offering a contract extension of sorts (Hall has one year left on his deal after 2013).

Wide receiver Santana Moss, who will turn 34 in June, is owed $6.16 million in the final year of his deal. Other players Washington could look to extend and in the process lower cap figures may include cornerback Josh Wilson and linebacker Brian Orakpo. Wilson, who is in the final year of his deal, carries a cap figure of $5.3 million. Orakpo’s contract, which carries a cap hit of $5.1 million, is voidable after this season.

Once they create cap space, Washington has pressing needs to meet on both sides of the ball.

The Redskins’ priority unrestricted free agents include linebacker and special teams captain Lorenzo Alexander, who just made his first Pro Bowl, and tight end Fred Davis, who had a career year in 2011 but missed much of last season with a torn Achilles’ tendon.

Lichtensteiger, the starting left guard, and right tackle Tyler Polumbus also have expiring deals. But it remains to be seen if Washington will allow them to walk and promote 2012 third-round pick Josh LeRibeus to the starter at left guard and pursue another right tackle in free agency.

Maintaining a strong offensive front is crucial considering Washington must protect franchise quarterback Robert Griffin III, who is coming off torn knee ligaments suffered in the team’s playoff loss to Seattle. The offensive line, expected to be an area of weakness at the start of last season, boasted great continuity as the same five players started for 16 of the 17 games and paved the way for an offense that ranked fifth in the league with 383.2 yards per game and fourth in scoring at 27.3 points.

But Washington’s most glaring weakness lies in its secondary, particularly at safety. Meriweather missed the first 10 games of last season with knee injuries and played only one half before suffering a torn anterior cruciate ligament in Week 11. The team was forced to use a rotation of players in his place, and free safety Madieu Williams, who is now a free agent, underperformed. As a result, Washington’s defense ranked 30th in the league against the pass.

The Redskins still have Meriweather and talented but troubled free safety Tanard Jackson under contract, but there’s no certainty to what kind of recovery Meriweather can make, and when precisely Jackson will be reinstated after serving a year-long drug suspension.

Washington also needs a third cornerback.

The free agent market offers a number of quality defensive backs with Charles Woodson, Brent Grimes, Aqib Talib and Dashon Goldson ranking among them. But it remains to be seen if the Redskins can afford any of them.