Exact details of the report were not made public.
"He is cooperating with SFPD and the reporting party," Officer Grace Gatpandan told ESPN.com. "The report was taken over the weekend, and he was mentioned in the report."
No arrests have been made.
TMZ Sports reported earlier in the day it was a domestic-related investigation.
The Raiders declined to comment to ESPN.com, though the team is forbidden from having any contact with Smith under the rules of his suspension, which was handed down in November 2015 after several incidents that included arrests and a substance abuse infraction.
"We are looking into the matter," Brian McCarthy, NFL vice president of communications, told ESPN's Adam Caplan on Tuesday.
Raiders owner Mark Davis has taken a strong stance against cases of domestic violence, saying the team has a "zero-tolerance" policy.
"It's just something we can't tolerate," Davis told the San Francisco Chronicle in 2015. "I don't know how to fix it in society but I know we can't have it on our team."
Raiders Hall of Fame receiver Fred Biletnikoff lost his daughter Tracey in 1999 when she was murdered by an ex-boyfriend, and the Raiders have been supporters of Biletnikoff's mission to provide a home for women in need. Davis presented Biletnikoff with a check for $50,000 in 2015.
Smith applied for reinstatement in the fall, but the league tabled discussion until this offseason. The NFL Network reported Smith could be reinstated in March, so long as he stays out of trouble.
"I'm back," Smith said last week on Instagram Live. "And there's nobody who can stop me."
Answering questions from viewers, Smith said, "You already know it. Raider Nation, we got this s---."
Should Smith gain reinstatement, he would be able to join the Raiders and reigning NFL Defensive Player of the Year Khalil Mack for the start of their offseason program April 17. Rookie minicamp is scheduled for May 5-7, with OTAs set for May 23-25, May 30-June 1 and June 5-8. Mandatory minicamp is scheduled for June 13-15.
Smith, the No. 7 overall pick of the 2011 draft by the San Francisco 49ers, has 47.5 sacks in 59 career games. He was released by the Niners in August 2015 following his fifth arrest since 2011 and third on suspicion of drunken driving.
Smith signed with the Raiders and played nine games in 2015 before he was suspended.
A video of a man purportedly holding a blunt on a Periscope account belonging to Smith showed up last offseason, though Smith denied it was him and eventually took down the video.
Raiders coach Jack Del Rio said late this past season he was "a little disappointed" after the league declined to reinstate Smith.
"Obviously, it's not my job to make a rule, but from everything I've gathered, he's done his duty to take care of all the things he needs to take care of," Del Rio said.
"I see some of the guys that have been allowed back. My question is what's the difference? It's always a question mark. If a guy has a chance, he should have a chance to make a living.
"I don't really agree with what's gone down, but it's not my job. We'll move on as a team. That's what we have to do, but I'm a little disappointed."