Speaking at a press conference at Örebro police station, police said the current suspect, 42, had been in the frame at an early stage in the investigation.
"We have investigated various potential motives, and this person has figured in one of these scenarios from the very beginning," said Dag Andersson at the Swedish police's National Murder Commission.
Deputy Chief Prosecutor Kristian Agneklev said he could not reveal the nature of Deniz's relationship with his suspected killer nor could he give details of the suspected motive.
Deniz, 40, was stabbed in the university's sports complex on December 11th last year. He died of his injuries two days later. Police in Örebro have questioned hundreds of people in a wide-ranging investigation into the murder.
Prosecutors are expected to decide whether to apply for the suspect to be remanded in custody after he has undergone further questioning on Thursday.