The Washington Redskins are poised to pay a hefty price to move into position to take Robert Griffin III.

FOXSports.com and ESPN.com reported Friday night that the Redskins have a deal in place to acquire the No. 2 pick in the NFL draft from the St. Louis Rams. ESPN.com said Washington will give up its first and second-round picks this year, plus first-round picks in 2013 and 2014 in the trade, which can't be completed until the new league year begins Tuesday.

The trade shifts the Redskins up four places from sixth in the April draft, leapfrogging any other team that would have an interest in the Heisman Trophy winner from Baylor. The Indianapolis Colts are expected to take Andrew Luck with the No. 1 pick.

The bold move demonstrates how badly the Redskins are in need of a franchise quarterback after two decades of struggles. Coach Mike Shanahan has already whiffed on three in his two seasons in Washington, with Donovan McNabb, Rex Grossman and John Beck combining to produce an 11-21 record.

The Rams were in the market to trade because they already have their franchise quarterback, 2010 No. 1 overall pick Sam Bradford. The Redskins had to make an offer they felt would outbid the quarterback-needy Cleveland Browns, who could have offered both the No. 4 and No. 22 selections in this year's draft.

Cleveland general manager Tom Heckert acknowledged Thursday he had talked to the Rams.

"We feel very comfortable staying at four and getting a good player there, and that could happen," he said. "And we feel comfortable in moving down and getting more picks, we really do. It's way early to start talking about this stuff."

By sacrificing four premium draft picks, Shanahan is reversing the plan he set in motion last year to stockpile picks to rebuild Washington's depleted roster. The Redskins, however, have plenty of space under the salary cap and can be aggressive in plugging their holes when free agency begins Tuesday.

Grossman and Beck combined to throw 24 interceptions last year, putting the Redskins just one behind league leaders Philadelphia and Buffalo on the way to a fourth consecutive last-place finish in the division. McNabb, acquired in a trade from the Eagles, was the starter for the first 13 games in 2010, when Washington went 6-10.

Griffin, therefore, will get to work with a coach who has a reputation for working well with quarterbacks and designing effective offensive schemes, but Shanahan will likewise rely on Griffin to help make the coach a winner again. Shanahan has won only one playoff game since John Elway retired after capturing the second of back-to-back Super Bowls with the Denver Broncos in 1998, and he hasn't been to the playoffs in his last five seasons as a coach.