Authorities spotted the 46-year-old in the North Rhine-Westphalia city but lost track of him as he entered a high-rise building, they said. Michalski is believed to have been hiding out there, they added.
Police also found a bag full of clothing that belonged to the escapees in the city centre.
Michalski's accomplice in the spectacular escape from a prison in Aachen on Thursday, Michael Heckhoff, 50, was captured in the same city by police on Sunday after witnesses reported seeing his getaway car.
So far the pair has forced five people to help them in their escape, and police believe there is nothing to stop Michalski from harming innocent bystanders while on the run.
“End your flight before people are hurt,” a public statement from Cologne police said.
On Sunday, police also arrested a prison guard on suspicion he helped in the escape of the two violent inmates from the maximum-security prison. The 40-year-old guard is suspected of having helped the men get through locked areas and providing them with loaded prison service weapons as well as ammunition, according to statement by the state of North Rhine-Westphalia.
The two had been serving life sentences for murder and attempted murder.