The controversial midfielder has been told he can leave St James' Park on a free transfer after the breakdown in talks over a new deal.
But the 28-year-old, who on Tuesday claimed he had been fined two weeks' wages, has suggested in another Twitter post he will not be pushed out against his will.
This charming man: Joey Barton has continued to ponder his future on Twitter
'Just because ur [sic] told to jump, it does not necessarily mean u have to. I may choose to stand perfectly still. It's my right.just a thought,' Barton, who has a year to run on his contract, said.
Barton then returned to the social networking site to quote Washington, the first President of the United States, in another thinly-veiled attack on the Magpies.
'Quote of the day: If the freedom of speech is taken away then dumb and silent we may be led, like sheep to the slaughter. George Washington,' he tweeted.
Lonesome: Joey Barton was forced to train on his own by Newcastle on Tuesday
Barton was forced to train on his own and fined two weeks' wages after he was told he can leave the club on a free transfer, with a year still left on his current ?80,000-a-week contract.
The controversial midfielder, who on Tuesday was seen leaving the training ground with a large cardboard box of personal items, paid the price for his own Twitter rants, although Newcastle are convinced they have made the right decision to sever ties with the 28-year-old, who they believe had becomea disruptive influence in the dressing room.
Barton was in talks with a Premier League club, believed to be Aston Villa or Tottenham, while Celtic have also initiated talks with the player, though that seems an unlikely move. He is looking for aclub that can propel him back into the England set-up and give him a shot at next summer's European Championship.
Bigmouth strikes again: Barton has landed himself in hot water over Twitter
Sources close to the player told Sportsmail that while he will listen to all suitors, his decision will not be financially motivated but for football reasons alone.
Barton feels he has already wasted too many opportunities at international level and he recognises that hiscontroversial past may have counted against him.
But he has one cap already and is determined to prove he is worthy of a place in the England team after impressing as much as he did for Newcastle last season. For that, he feels, he needs a platform that will help him catch Fabio Capello's eye.
Well read: Barton quoted author George Orwell
Barton was reserved in his Twitter dealings yesterday, announcing that he was 'made to train alone, how predictable' and later 'Ha ha the inevitable, 2 weeks wages fine has just arrived. Needless to say it shall be appealed forthwith. ?kicking aman whilst hes down ha'.
Before that the former Manchester City man became possibly the first footballer to quote 1984 author Orwell, adding: 'In times of universal deceit telling the truth will be a revolutionary act'.
Meanwhile, Jose Enrique will follow Kevin Nolan and possibly Barton out of Newcastle after Liverpool agreed a ?10million deal for the Spanish defender.
And his pending departure comes as Newcastle look to become the first club to issue a blanket ban on their players using Twitter.
Liverpool saw off late interest from Chelsea to seal the deal for contract rebel Enrique, who will take KennyDalglish's summer spending to ?50m and ?107m since Andy Carroll left Newcastle for Anfield in January.
Get out of Toon: Jose Enrique will join Liverpool after the clubs agreed a ?10m fee
The loss of the popular Spaniard, whohas refused to open talks with Newcastle over a new contract and was fined last week for his Twitter attack, will be another huge blow to supporters who are understood to be planning a protest at St James's Park this weekend.
Manager Alan Pardew held a meeting with players after training yesterday and said the club would be lookingto impose a ban on the use of Twitter in future.
As well as Barton and Enrique, Nile Ranger, Danny Simpson and Wayne Routledge, who was sold to Swansea yesterday, have Twitter accounts.
CLICK HERE TO SIGN UP FOR OUR FREE FANTASY FOOTBALL GAMEToon's tweet revenge! Enrique follows Barton out of Newcastle with ?10m Liverpool switchWhy he's no ordinary Joe: Sportsmail explains why Barton is a wanted manBarton banished! Toon force Joey to train alone as Spurs lead chase for freebie star