A Twitter user, believed to be a 17-year-old Liverpool fan who works at a supermarket, tweeted: "I want to punch perch in his nigger head!"
The tweet ended by calling the Newcastle defender "a coon".
Student Liam Stacey was jailed last week for abusing the Bolton player Fabrice Muamba.
Stacey, 21, was jailed for 56 days after he admitted inciting racial hatred over remarks about the midfielder, who at the time was critically ill following his collapse during an FA Cup tie against Tottenham.
A Durham Police spokesman: "Northumbria Police contacted us yesterday afternoon after a member of the public complained about allegedly racist comments posted on Twitter.
"As the complainant lives in County Durham the matter was referred to Durham Constabulary and an appointment has been made for an officer to visit them and take further details."