HOUSTON — The A’s, leading the major leagues in errors by a large margin, are considering reuniting with longtime infield coach Ron Washington, The Chronicle has learned.

The A’s have made 43 errors, and shortstop Marcus Semien has committed 15 of them, putting him on pace for 59 this season. Washington is known as a terrific infield coach, turning shortstop Miguel Tejada and third baseman Eric Chavez into top-notch fielders in 1998-99.

Because the A’s have a full complement of coaches on the big-league staff, Washington is likely to take on a special-instructor role to work with Semien and Oakland’s other infielders.

Mike Gallego is expected to remain the A’s third-base coach and infield coach, although he has had a rough week, getting Stephen Vogt thrown out to end Friday’s game against the White Sox. Two more A’s players were thrown out at home in the second inning Tuesday night, although Brett Lawrie appeared to be going on his own in trying to score from second base on an infield single by Sam Fuld.

Washington stepped down as the Rangers’ manager in September and held an emotional news conference in which he said he had cheated on his wife, Gerry, and needed to mend his relationship with his family. While the Rangers’ manager from 2007-14, Washington took Texas to the World Series in 2010 and 2011, the best seasons in franchise history.

Washington told the Rangers’ front office and ownership in 2009 that he had used cocaine during that season, and the team retained him after that admission.

While Washington was the A’s infield and third-base coach from 1997 to 2006, Tejada was named the 2006 American League MVP and Chavez had a run of six consecutive Gold Glove seasons at third base. In recognition of Washington’s work with him over the years, Chavez presented his 2004 Gold Glove trophy to Washington with the inscription, “Not without you, Wash.”

A key scene in the movie “Moneyball” involves Washington teaching Scott Hatteberg, a catcher, how to play first base. Hatteberg’s successful position conversion is considered one of the reasons for Oakland’s success in 2002.

Washington, 63, has been serving as an assistant coach at the University of New Orleans this season.

Susan Slusser is a San Francisco Chronicle staff writer. E-mail: sslusser@sfchronicle.com Twitter: @susanslusser