Griffiths has not made a first-team appearance for Posh since April 2010, spending the best part of almost three years on loan at Chesterfield, Crawley, Rotherham and more recently Plymouth, where he enjoyed a month-long stay towards the end of 2012.
The 27-year-old is craving regular first-team football and is looking to sever all ties with Darren Ferguson's side before the transfer window closes.
He told Sky Sports: "I enjoyed my spell with Plymouth earlier this season but their regular left-back regained fitness during my time there, so I'm hoping for something a bit more permanent this time.
"Even if it is just until the end of the season I'd be happy because sitting on the sidelines here at Peterborough just isn't me. I enjoy playing the game far too much for that so if anyone needs a left-back, I'm their man.
"The club are willing to let me leave on a free transfer this month, so hopefully there will be some interest and I can start playing football again.
"The loan spell at Plymouth helped me get my match sharpness back up and I'm training every day with Peterborough, so I could be thrown straight into the team should the club want me to."