Saeb Erekat said Abbas and Olmert would also meet when the Israeli leader returned from a trip to the United States.
But an official in Olmert's office denied that any meeting had been planned, although he said the two spoke by telephone earlier on Friday.
Erekat said Abbas called Olmert to congratulate him after his new government was sworn in the day before.
"He (Abbas) spoke to him about peace partnerships and advancing peace moves," Erekat said.
A statement from Olmert's office did not mention any discussion of peace talks, now seen as remote since Hamas took office in late March after trouncing Abbas's long-dominant Fatah movement in January elections.
Israeli officials have said Olmert will visit Washington later this month where he is expected to present to President George W Bush his plans to impose Israel's final borders by 2010 if peacemaking with the Palestinians remains frozen.
Abbas has said he is ready to resume negotiations with Israel immediately and proposed opening "a back channel of talks" to US officials and Shimon Peres, a former Israeli prime minister who has spearheaded peace efforts in the past.
Shimon Peres has spearheaded
peace efforts in the past
Elder statesman Peres, a minister in the new government, has also said Olmert is likely to meet Abbas after his US visit.
Olmert said his coalition government would prefer peace talks with the Palestinians over unilateral moves.
But he reaffirmed on Thursday that Israel would not deal with a Palestinian Authority led by Hamas unless Hamas recognised the Jewish state and renounced violence.
Israeli officials have also questioned whether Abbas, a moderate who seeks a two-state solution to end the conflict, can deliver on any peace agreements with Hamas in power.
Hamas says talks with the Jewish state will be a waste of time.