Washington is one of five candidates who have been interviewed in the search to replace manager Buck Showalter, who was fired after an 80-82 season.
Texas bench coach Don Wakamatsu and Japan Series championship manager Trey Hillman spoke this week with general manager Jon Daniels and Rangers owner Tom Hicks.
New York Mets third-base coach Manny Acta and Phillies minor league manager John Russell, a former Rangers catcher who caught one of Nolan Ryan's seven no-hitters, have also interviewed. But neither met with the owner.
Washington has been a coach with the A's the past 11 seasons. He also is a candidate to replace fired Oakland manager Ken Macha.
Hillman, an Arlington native, led the Nippon Ham Fighters to their first Japan Series title since 1962. He was the Rangers' director of player development for one year before spending the last four seasons in Japan.
The Rangers fired Showalter after their sixth losing record in seven years since last making the playoffs in 1999. Showalter was 319-329 in four seasons.