Abbas left Monday on a trip to Germany, Belgium and Italy, the Hebrew daily said.
The trip comes amid reports from Palestinian sources that Israel is considering halting American-initiated peace talks and a pending prisoner release, Maariv said.
"Abbas and the Palestinian leadership hear the opinions in Israel that are talking about the possibility of freezing talks because of recent events and are preparing an alternative plan ... with the goal of winning international recognition for a Palestinian state," the report said.
Palestinian and Israeli negotiators have met several times in the American-sponsored talks, which have a goal of reaching a peace agreement in nine months.
Notable deaths of 2014 [PHOTOS]