Barton was released from prison yesterday amid calls from some quarters that he should be sacked by United.
Ashley could, by rights, pull Barton's contract forthwith without paying up the further three years of that contract, due to the player spending 74 days behind bars.
But the club has £6m tied up in the player ... although the sell-on figure has reduced to probably £1m.
However the midfielder was back training with United today and the club issued the following brief statement:
"Newcastle United officials can confirm that they have met with Joey Barton today (July 29) following which it has been agreed by everyone involved that Joey will remain with the club.
"The club will not be making any further comment on the matter."