The comments by Armenian Foreign Minister Edward Nalbandian followed similarly optimistic remarks by his Turkish counterpart last week. The two countries have no diplomatic ties and in 1993 Ankara closed their land border in a show of solidarity with ally Azerbaijan over the conflict in Nagorno-Karabakh region.
Relations have been haunted by the 1915 incidents, which ex-Soviet Armenia says amounted to "genocide". Ankara denies there was genocide.
But there has been a flurry of diplomacy in recent months, including a visit by Turkish President Abdullah Gül to Yerevan in September to attend a football match between the two countries.
"We are very close to normalising Armenian-Turkish relations," Nalbandian told a news conference, Reuters reported. "We can take the next step and resolve the issue if Turkey, like Armenia, approaches it without preconditions and opens the border," he said. "After the border opens, we are ready to form a commission in which we can discuss issues relevant to both countries."
Since its war with Russia last year raised questions about Georgia's role as a safe transit route for oil and gas exports from the Caspian Sea, Armenia is being eyed as a potential alternative. Better ties between the neighbours would also boost Ankara's European Union membership bid.
Turkish Foreign Minister Ali Babacan said in a television interview last Friday normalisation of relations between Armenia and Turkey and Armenia and Azerbaijan was no longer "a dream." "I can easily say we have never come this close to a plan regarding the final normalisation of relations with Armenia," he said.