The League One outfit are keen to bolster their squad during the January transfer window with the 23-year-old midfielder.
According to The Scotsman's sister title Peterborough Telegraph, manager Darren Ferguson is keen on two players with Docherty on the radar following his success on loan at Shrewsbury Town in the same division last season.
He played 50 times for the League One side, netting ten times.
It is understood Docherty opted against joining Peterborough in the summer as he tried to win a place in the Rangers midfield under Steven Gerrard.
He has featured just five times this season, his last appearance coming in August, while he has been on the bench only once in the league.
Signed for around £600,000 from Hamilton back in January 2018, Docherty has struggled for first-team football with just 19 appearances for the first-team .
Posh are currently third in League One, eight points off the top of the table.