Officers investigating the murder of Ashling Murphy said "significant progress" was being made in the case.
The development comes after the Irish police identified a new person of interest, who is believed to be in a hospital.
He is receiving treatment and officers are waiting to speak to him.
They have released a description of the suspect and renewed their appeal for information on any suspicious activity from the public.
The 23-year-old teacher was found murdered after going for a run on the banks of the Grand Canal in Tullamore, Ireland, last week.
Her funeral mass took place at St Brigid's Church on Tuesday.
The Irish Police have announced they believe the development of DNA profiles will play an integral role in the search for Ms Murphy's killer.
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