The man detectives want to speak to in relation to the murder of Polish student Angelika Kluk is in hospital.
Peter Tobin was the last person believed to have seen the 23-year-old alive. Her body was discovered at St Patrick's Church in Glasgow's Anderston area on Friday, where she had been staying since July.
Tobin, a 60-year-old handyman at the chapel, was arrested in London on Saturday. He has been held on an unrelated matter for an outstanding warrant under Section 84 of the Sexual Offences Act 2003.
Detectives from Glasgow had been due to bring him back for questioning, but that, due to a medical condition, Tobin was not fit for travel.
It is believed he has previously been treated for a heart condition.