Finnish authorities believe that the man, who murdered a family in Åmsele, northern Sweden in 1988, may have tried to return to Sweden.
Swedish police have put out a nationwide alert, but say there is no specific information to indicate that he has entered the country.
“We have no intelligence about that, and we wish to make that clear as there was various information circulating yesterday,” said Swedish police spokesman Varg Gyllander.
A number of tips were received by police on Tuesday evening, but none have yet been judged to be particularly hot. The National Criminal Investigation Department in Stockholm is now collating information about Valjakkala, and preparing for the fact that he might come to Sweden.
“He has contacts in Sweden, there’s no doubt about that. Last time he escaped from prison he was shown to be on his way to Sweden. But there’s nothing that indicated that [he is doing that] at the moment,” Gyllander said.