Israeli Foreign Ministry spokesman Mark Regev had no comment on the report.
Palestinian negotiator Saeb Erekat said delegations led by Abbas and Livni would meet next week, but he wouldn't say when or what would be on the agenda, reports AP.
It would be the second meeting between the two since the militant Hamas organization swept Palestinian elections in January. The two last met in May at the Egyptian resort of Sharm el-Sheik.
Since that time, Israel waged an inconclusive war against Hezbollah guerrillas in Lebanon and shelved its plan to withdraw unilaterally from much of the West Bank. Hamas, meanwhile, pressured by crippling international sanctions meant to force it to temper its militantly anti-Israel stand, agreed last week to form a coalition government with the Fatah Party led by Abbas, who favors renewing peace talks with Israel.