Preliminary analysis of the blood matches DNA taken from Sjodin's toothbrush, the Star Tribune of Minneapolis reported, citing two sources close to the investigation.
CBS News Early Show National Correspondent Jon Frankel reports blood found on a knife discovered in the car's trunk also matches Sjodin's.
It's also been reported that a knife sheath was found near Sjodin's car in the parking lot of the Grand Forks shopping mall where she disappeared.
That sheath could only belong to a particular knife sold exclusively as a set in a home improvement store in Grand Forks, one of the sources told the Star Tribune.
Sjodin, 22, of Pequot Lakes, Minn., was last heard talking to her boyfriend on a cell phone Nov. 22 after the University of North Dakota student left her job at a Victoria's Secret.
Alfonso Rodriguez Jr., 50, has been charged with kidnapping Sjodin. Evidence in the case, which was sealed by a judge after Rodriguez's arrest, should be released Tuesday when the affidavit of probable cause is opened.
Rodriguez's maroon, four-door 2002 Mercury Sable was impounded by authorities before his Dec. 1 arrest in Crookston, Minn.
David Dusek, Rodriguez's public defender, has said his client stated he had nothing to do with Sjodin's disappearance.
Frankel reports it is believed that Rodriguez has been driving around with investigators but sources say they would not characterize him as cooperating.
Bail has been set at $5 million, but Rodriguez has chosen to stay in jail because of fears for his safety. He faces a preliminary hearing Feb. 4 and arraignment Feb. 6.
Sjodin's father said Monday he was dismayed to find that police recovered a knife from Rodriguez's car. But given Rodriguez's criminal past, he said he was not surprised.
"You know what? It's probably true," Allan Sjodin said. "That's his modus operandi."
Rodriguez is a convicted rapist who has a history of attempted kidnapping with adult women, and has used a weapon in at least one assault. He was registered as a predatory offender, the classification for those believed to be at the highest risk of committing another sex crime.
Rodriguez was released from a Minnesota prison in May after serving 23 years for an attempted abduction in 1979. Wayne Swanson, who prosecuted Rodriguez, said Rodriguez tried to abduct a woman off the street, and stabbed her when she fought back.
Allan Sjodin said he is still determined to find his daughter alive.
"I have one mission here," he said. "It's the same mission I've been telling everyone about since day one, and that's to find Dru."
Bob Heales, an investigator hired by the Sjodin family, said no one is quitting.
"I think there are just too many possible scenarios," he said. "Too many things we still need to look at ... we're a long ways away from that point."
Meanwhile, investigators said they planned to expand their search for Sjodin to areas south of Grand Forks this week.
Police Capt. Mike Kirby said searches would continue until officials have firm reason to believe Sjodin is dead.
"We are committed to this. The family is out and we will be out," Kirby said.
Searchers Monday included Sjodin's uncle, who noted that volunteers also were pitching in.
"Some of the guys we don't even know," Lowell Sjodin said. "It's this part of the country, I think. Everyone just pulls together."