According to The Chronicle, the Greek outfit are offering around £300,000 for the 21-year-old, who enjoyed his best top-flight season to date on loan with them last year.
The report claims that Abeid could have been the one Newcastle player out on loan to be given another chance by Alan Pardew. However, Panathinkaikos are confident that a deal can be pushed through over the next few days.
The Greek Cup winners' squad have been told to report for training on Saturday and French-Algerian Abeid is said to have been told to join them.
Abeid scored 10 goals in 38 games for the Greeks in the last campaign.