Northumbria Police confirmed they have begun inquiries after they were informed in the early hours of an allegation received by Staffordshire Police.
A spokeswoman said: "Just after midnight police received a complaint of racist comments that had been made on Twitter.
"Officers are carrying out inquiries."
Collymore, 40, originally from Cannock, Staffordshire, played for a string of top clubs, including Liverpool, Aston Villa and Nottingham Forest.
He works as a broadcaster for talkSPORT, campaigns against racism and is a supporter of the charity Depression Alliance.
It was believed the allegedly racist tweets were sent by someone in the Tyneside area.