Montreal police have not publicly linked the remains, which have yet to be confirmed as coming from a human, to the case.
They have not given the source of the tip.
However, a police source told The Associated Press that the remains appear to be a human head.
Magnotta, 29, is accused of the murder and dismemberment of Lin, a Concordia University student from China, in May.
Lin's remains were mailed to locations in Ottawa and B.C., and were also discovered behind a Montreal apartment building where Magnotta had been renting a unit. Parts of his body have not yet been located.
Police have been in contact with Lin's family and have said that finding the rest of his remains was a priority. His family held a private service for the 33-year-old last week at Concordia.
Following an international manhunt, Magnotta was arrested in Berlin after an employee at an internet café recognized him from the intense media coverage. He was returned to Canada in June and has pleaded not guilty to all charges.
Testing could take days
The latest discovery of remains, in Angrignon Park in southwest Montreal, happened Sunday afternoon.
Investigators set up a wide perimeter as they scoured an area into the evening.
Police are now waiting for further analysis of the remains, which could take several days, to determine if they are from a human and if they are linked to the case.
"For the time being, it is still too early to confirm anything," Const. Anie Lemieux said.
Magnotta will face a preliminary hearing next March, where part of the evidence against him will be heard. He has chosen a trial by jury.