Matthew Baker, 28, who along with James Whitlock, 31, fled the Victorian-build Category B prison in London on Monday, was said to have used a phone that had been smuggled into the jail to send the messages.
He also posted pictures of himself on the website, the Sun reported.
It is very likely that they are being assisted by others, possibly with somewhere to stay, clothing and money; in order to evade captureDCI Steve Heatley
On the Facebook profile - which was taken down after the newspaper flagged its existence - one message reportedly told his enemies: "I know where you live".
The poorly-spelled post read: “Let’s get one thing straight to anyone who wants to say anythink behind my back.
“I know your names n where yous live n believe me we’ll meet again one day n i dont forget nothic just remember that yous know who yous are.”
Baker was found guilty of attempted murder two weeks ago, having stabbed a man in Dagenham following a dispute.
He had been remanded for sentencing later this week. Whitlock was on remand after being charged with conspiracy to burgle over 19 alleged ATM thefts.
The men - understood to be cellmates - reportedly used diamond-tipped cutting equipment to break through bars before scaling a perimeter wall.
It was claimed that their beds were stuffed with pillows to make it look like they were asleep.
The Met Police said on Tuesday night that it was likely fugitives Whitlock and Baker were being offered sanctuary by friends, and that the investigation was moving "at a fast pace", although the pair remained on the run.
DCI Steve Heatley said: "We have received a positive response to our appeals and the flow of information from the public so far has been very good.
"However, I would continue to encourage anyone with information about the current whereabouts of these two men to contact either the police or Crimestoppers in confidence, as soon as possible.
"It is very likely that they are being assisted by others, possibly with somewhere to stay, clothing and money; in order to evade capture.
"I would appeal to anyone who is helping that they are potentially committing a crime and would encourage them to contact us so that we can bring this matter to a safe and swift conclusion."