Norris was released by Leeds at the end of January and it seems that he has not had to wait long to find a new club.
The 33-year-old has apparently been identified as a player who could aid Darren Ferguson's side's faltering campaign, with his experience considered to be a quality Posh need to add to their squad.
What's the impact for Posh?
Peterborough United's season has been threatening to peter out into mediocrity for some time, but this transfer seems like a rather odd one.
Norris played just twice in 18 months towards the back end of his time at Leeds and it is likely to take him a considerable amount of time before he is fully match sharp.
It is also a transfer which appears to stray away from Posh's policy of bringing in 'young and hungry' players.
Peterborough have been famed for their ability to pluck raw talent out of the non-league and develop them into stand-out Football League stars, but Norris is at the other end of his career.
The midfielder had been showing signs of age at Elland Road, with his performances well short of the quality required to make an impression, and he will arrive at the ABAX Stadium with a point to prove, should a deal go through today.