Denard Span could begin rehab games on Thursday and return to the Nationals as soon as Saturday.
The outfielder said he feels even better than Monday and hopes to be ready to return by Saturday.
The center fielder will rest again on Sunday and will be evaluated Monday after physical activity.
The center fielder is suffering from mild concussion symptoms after a collision on Friday.
Entering the final guaranteed season of his contract with the Nationals, Span says he would like to remain in Washington.
The Nationals general manager says the interest in both relievers has been informal.
The center fielder is honored as the Nationals' best defender in 2013.
Both Nationals players finish as finalists, losing the awards to Andrelton Simmons and Carlos Gomez, respectively.
Winners for the award will be announced on Tuesday.
Davey Johnson wants to make the Cardinals have to earn their NL Central title.