Williams is hopeful that Gonzalez -- who has been working out and throwing on his own this spring -- will join the team on Wednesday.
"It's a little bit late in the game, but he told us he's been throwing and he's ready to go," Williams said. "We'll see when he gets here what, in fact, he's done and where he's at."
Gonzalez aims to become the second left-hander out of the Nationals' bullpen behind Jerry Blevins, acquired from the A's in a December trade. Blevins, 29, recorded a 3.15 ERA in 67 appearances in 2013.
Xavier Cedeno, 27, is also a candidate for that spot. Cedeno recorded a 1.50 ERA in 11 relief outings with the Nationals last season and compiled an even better mark of 1.31 in 39 appearances with Triple-A Syracuse.
Cedeno pitched two scoreless frames in Spring Training action before Tuesday's game against the Braves.
Williams is also open to using right-hander Tyler Clippard against left-handed batters. Clippard held opposing lefties to a .152 average last season.
Ideally, every manager would employ two lefties in the bullpen, Williams said, but roster configuration will require him to meditate on the process.
"You look at it and say, 'Do you want two lefties? Do we need two lefties?'" Williams said. "'What does the first lefty offer you? Does he have the ability to get right-handers out as well? Is he a longer guy that's resilient that [can throw] an inning-plus to two innings in a game? How does he bounce back?' All of those questions come into play."
Washington hopes that if Gonzalez makes the team, he can channel the performance he provided en route to the club's first National League East title in 2012. That season, he posted a 3.03 ERA -- his lowest in the past four seasons -- in 47 appearances out of the Nationals' bullpen.
Joe Morgan is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.