A federal judge says she might toss some of the strongest evidence against Barry Bonds, a blow to prosecutors trying to prove the home-run king lied when he denied knowingly using performance-enhancing drugs.

U.S. District Judge Susan Illston said her ‘‘preliminary thoughts’’ were to exclude from trial three 2000-2001 positive drug tests that prosecutors say belong to Bonds unless there is a direct link that the urine samples came from the former San Francisco Giants slugger.

‘‘If there’s no testimony to establish that, I don’t think any of them work,’’ Illston said.

The only person who can do that seems to be Bonds’ personal trainer, Greg Anderson, who spent more than a year behind bars for refusing to speak to a federal grand jury investigating Bonds. And Anderson’s attorney, Mark Geragos, has said his client will not testify against Bonds at the trial, scheduled to start March 2.

Without someone to authenticate that the test results were from Bonds’ urine, Illston said claims that the tests were Bonds’ were ‘‘classic hearsay.’’

Based on the same logic, Illston said she likely also would exclude a doping calendar and other papers seized by federal investigators at Anderson’s home.

She was inclined, however, to allow a recorded conversation between Anderson and Bonds’ former personal assistant Steve Hoskins in which they discuss injecting steroids. Hoskins recorded the conversation without Anderson’s knowledge.

Illston will issue a formal decision on the evidence discussed Thursday at a later date. She also will hold a separate hearing on whether to allow testimony from expert doctors the government hopes would persuade a jury that changes in Bonds’ body were due to steroid use.

According to court documents, Bonds tested positive on three separate occasions in 2000 and 2001 for the steroid methenelone in urine samples; he also tested positive two of those three times for the steroid nandrolone.