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Running back Frank Gore is scheduled to be a free agent for the first time in his NFL career. And, perhaps, his biggest fan is now in a decision-making role with another professional team.

Scot McCloughan, who picked Gore at the top of the third round in the 2005 draft, was introduced as Washington’s new general manager on Friday.

McCloughan has a high opinion of Gore as a football man. In the past, he talked about employing Gore as a scout after his playing career ended. And even after McCloughan left the 49ers, Gore often called him to act as a sounding board, according to a league source.

Gore, who turns 32 in May, is scheduled to become an unrestricted free agent on March 10. The 49ers have exclusive negotiating rights with him until then. General manager Trent Baalke expressed a desire to re-sign Gore, and Gore said he wants to come back. But Gore is also eager to see what direction the 49ers go with their next coach.

[RELATED: McCloughan: Washington further along than when he joined 49ers]

Conceivably, Gore could fit with Washington as a backup. Alfred Morris returns next season as Washington’s top running back. Backup Roy Helu is scheduled for free agency. With the 49ers, Gore could see more of his playing time distributed to Carlos Hyde. Gore had his eighth 1,000-yard season in 10 years with the 49ers in 2014.

Washington could also serve as a landing spot for 49ers outside linebacker Ahmad Brooks, whom San Francisco is not likely to retain at his scheduled $7.3 million price tag for next season. McCloughan originally acquired Brooks in 2008 with a waiver claim. Brooks’ late father, Perry, played his entire seven-year NFL career with Washington.

Another player McCloughan acquired who could be available this offseason is tight end Vernon Davis. After a lackluster season, Davis’ roster spot with the 49ers could be in jeopardy for next season due to his scheduled $4.95 million salary. McCloughan selected Davis with the No. 6 overall pick in the 2006 draft.

Second-year tight end Jordan Reed had 50 catches for 465 yards and no touchdowns for Washington. One season after catching 13 touchdowns, Davis’ production dropped to career-worst levels of 26 receptions for 245 yards and two touchdowns.