Mehmet Ali Talat told the Greek Cypriot Phileleftheros newspaper on Sunday that he would talk to Papadopoulos on any matter, but expected it to be over the issue of missing persons.
It would be the first meeting between the two since a UN reunification blueprint was rejected in a referendum in April 2004. Peace talks have been shelved ever since.
A meeting on the more than 2,000 missing Greek and Turkish Cypriots is seen as necessary to help spur both sides to consider new reunification talks.
Papadopoulos has said he will meet Talat, leader of the breakaway Turkish Republic of Northern Cyprus which is recognised only by Ankara, to talk only about the missing.
"Such an approach is somewhat dangerous, because this is the only issue which is progressing and on which both sides are cooperating... so essentially we won't discuss anything, because there's no problem," Talat said.
Meanwhile, Cyprus has discovered human remains thought to be those of Turkish Cypriots who went missing during clashes on the ethnically partitioned island in 1963 and 1964.
A source close to the UN-backed Committee for Missing Persons said on Monday that the remains were discovered in the southeast of the island at a site forensic experts started excavating on June 2.
"They found remains, but we are not in a position to say anything until further tests are carried out," said the source, who spoke on condition of anonymity.
Talat (R) said he hopes to meet
Papadopoulos (L) in July
Asked if they were human remains, the source said: "Yes." The source was not in a position to say how many individuals were thought to be buried at the site.
If verified, it would be the first known case of a Turkish Cypriot multiple grave being found on the Greek Cypriot side of the island since Cyprus was partitioned three decades ago.
The missing persons issue is a highly charged one which has added to decades of mistrust between Greek and Turkish Cypriots on the island, which Turkey invaded in 1974 after a brief Greek-inspired coup.
Some 1,500 Greek Cypriots and some 800 Turkish Cypriots are unaccounted for.