"The president insists on not running in the upcoming election," an official from the Palestine Liberation Organisation (PLO) executive committee said on Thursday.
Another PLO official said Abbas will give a speech later on Thursday explaining his decision not to run.
Abbas recenty issued a decree announcing that presidential and parliamentary polls would take place on January 24.
But the Hamas-run interior ministry in the Gaza Strip ordered Palestinians in the territory not to take part in elections.
The interior ministry said in a statement the elections had been called "by figures who do not have the right to declare it".
Ehab Al-Ghsain, a Hamas interior ministry spokesman, said that Gazan officials had been instructed not to co-operate with Abbas's efforts to stage the vote.