The woman, who is in her 20s, was jogging on a path through El Palo Alto Park near 102 Palo Alto Ave. around 6:55 a.m. when a man approached her from behind.
The man wrapped his arms around her, grabbed one of her breasts and tried to pull her down, police said.
The woman screamed and was able to free herself, though she fell in the process, police said. The man turned and jogged away on the same path, then headed south on the Alma Street.
The victim, who was not injured, got up and followed the suspect while calling police. The suspect was last seen jogging east on Hawthorne Avenue. Officers searched the area with a K-9 unit but were unable to find the man.
Police said they believe the man who grabbed the jogger this morning may be the same man who grabbed a woman's buttocks in the 600 block of Fulton Street at about noon on Aug. 20, and grabbed a different woman's breast at the Stanford Shopping Center shortly after noon on Aug. 29.
"We are concerned about all of these events, but we are particularly concerned about this one, as it appears as though the suspect's behavior may be escalating," police Lt. Zach Perron said.
Sketches of the suspects in the two previous cases are posted on the Police Department's Facebook page at www.facebook.com/PaloAltoPolice.
The suspect is described as possibly Middle Eastern or Hispanic, around 40 years old, and 5 feet 9 inches tall, with a medium build and thick hair.
The woman told police the man was dressed like he was out for a jog, wearing a light gray long-sleeve shirt and dark gray or black running pants.
Police said they do not believe the suspect is the same one who was involved in a sexual battery on the Stanford University campus on Sept. 12.
Police recommended that women jog in pairs or groups when possible, avoid covering both ears with headphones, carry a cellphone and stay in well-traveled areas.