Since Cole was demoted less than 10 days ago, the Nats can add the 25-year-old right-hander only to replace an injured player. An announcement on a corresponding move is expected to come Monday.
Cole is 1-4 with a 4.50 ERA in five starts this season for the Nationals. Strasburg (11-4, 2.90 ERA) is coming off of his best outing of the season, having thrown just his second career complete game, a six-hit shutout of the Marlins that included eight strikeouts and just one walk.
Strasburg's gem against the Marlins last week was just his third start since his return from a nerve impingement in his right forearm. The injury forced the righty to go on the DL and miss nearly a month.
Baker's comments came a day after staff ace Max Scherzer left his start early after being hit in the left leg by a comebacker. Despite the timing of the Cole announcement, Baker said Scherzer is expected to make his scheduled start Thursday and was only experiencing soreness Sunday.
Washington (82-54) holds a 15-game lead over the Marlins in the NL East but dropped three of four to the Brewers in Milwaukee.