Mike Garafolo of NFL Network reported the news. Washington would likely take a quarterback if the team chose to move up, with Ohio State's Dwayne Haskins and Missouri's Drew Lock being the most prominent names.
Washington already traded for Case Keenum this offseason and will bring back Colt McCoy. Their quarterback situation took an unfortunate turn when Alex Smith suffered a career-threatening leg injury last season. Smith is not expected to play in 2019.
Washington currently has the No. 15 pick in Thursday's first round and would have to give up significant draft capital to move into the top five.
They already traded their fourth-round pick for safety HaHa Clinton-Dix, who spent all of one season in Washington before leaving for the Chicago Bears. They also forfeited a sixth-round pick when they took Adonis Alexander in the supplemental draft.
Including supplemental selections, Washington will make nine picks in the 2019 draft. According to the classic Jimmy Johnson draft-pick calculator, Washington would have to give up the equivalent of their first-, second- and third-round picks to move up to No. 5.
Something like Washington's first and second in 2019, along with a 2020 second and another mid-round pick, might be enough to move the needle for a team in the top five.
Whether that's a smart move is very much up to your evaluation of the 2019 quarterbacks. Haskins, Lock and Duke's Daniel Jones each have significant red flags, whereas the 2020 crop of signal-callers is much more highly regarded.
Washington doesn't appear to have the roster of a playoff team next season, so it may be smarter to hold off before potentially trading up next season if they land outside the top five.