The suspect is a 24 year-old man of Lebanese origin, reported daily newspaper Dagens Nyheter (DN), and Sweden's Foreign Ministry (Utrikesdepartementet, UD) has confirmed the arrest.
A police spokesman said he could not deny or confirm the reports because it was a "sensitive political issue".
"This is an issue of security which we take very seriously and we cannot comment any further," the spokesman told AFP.
Online news website Sigmalive said the police were tipped off by foreign intelligence services and the man -- who came to Cyprus as a tourist -- was arrested in his hotel room last week.
It said the suspect appeared before a closed court for a second time on Friday where he was detained in police custody for another seven days.
Cyprus state television said Israeli intelligence agents had supplied information to the Cypriot authorities regarding the suspect. It did not elaborate.
Police are trying to unravel the level of involvement of the suspect, the intended targets and whether he had accomplices on the island.
According to Sigmalive the man arrived on the island to plan and orchestrate the blowing up of a plane or a bus. Local daily Phileleftheros said notes with details of Israeli aircraft were found in his possession.
State radio said the suspect was staying in the southern coastal resort of Limassol and took photographs of Israeli interests.
Police have made no official public statement about the arrest or the investigation.
Cyprus had seen attacks against Israeli interests in late 70s and early 80s, but since then the island has been viewed as neutral ground for unofficial Mideast peace contacts.
The 24 year-old has received legal representation, and his case will be followed by the Swedish embassy in Nicosia, reported DN.