On Tuesday, the team got a chance to learn more about both prospects.
Griffin was in Washington on Tuesday and met with the Redskins, and Luck was scheduled to arrive in the area on Tuesday night to meet with the team, a league source told ESPN NFL Insider Adam Schefter.
Luck was going to Washington from Indianapolis; Griffin was scheduled to leave Washington on Tuesday afternoon, but it was not clear where his next visit would be.
Each NFL team is allowed visits with up to 30 prospects before the draft.
The Indianapolis Colts, who own the No. 1 overall pick, had a private workout with Luck at Stanford last week and are expected to select the former Cardinal quarterback with that pick.
Colts owner Jim Irsay posted on Twitter how impressed he was with Luck after visiting with the quarterback on Tuesday.
"Met with A Luck#12 n Indy 2day for 3 hrs;it's easy 2c why the #1 pick n this Stanford phenom has been synonymous with each other 4over 2 yrs," he wrote.
Heisman Trophy winner Griffin won't hold a private workout for the Colts or Redskins, as the former Baylor quarterback believes there's no need to risk an injury when he's assured of being selected in the top two spots, a league source told Schefter last week.
Irsay has said the Colts will take a quarterback with the No. 1 pick in this month's NFL draft. And while there have strong indications the Colts will take Luck, neither Irsay nor general manager Ryan Grigson have said the Stanford quarterback will be the choice for Indy.
Luck is considered the most NFL-ready quarterback since 1998 when Peyton Manning was taken No. 1 overall by the Colts. Indy released Manning last month, a move that led many to believe Luck would be the No. 1 pick on April 26.
Information from The Associated Press was used in this report.