But Johnson insisted no deal had yet been agreed for the 26-year-old.
Peterborough's director of football Barry Fry said he was expecting Davies to join the Cobblers after the player worked with Johnson at Posh and Yeovil.
"Of course I'm well aware of Arron, he's a spinning plate for us," Johnson told BBC Radio Northampton.
"That's all I can say about it at the moment. He's currently on holiday so things haven't been set down and talked about yet.
"But, yes, I'm very aware of Arron Davies and he's very aware of us."
Davies began his career at Southampton and made more than 100 appearances in three seasons at Yeovil before moving to Nottingham Forest in 2007, Brighton in 2009 and back to Yeovil before moving to Posh last July.
The Cobblers recently agreed a two-year deal with full-back Seth Nana Ofori-Twumasi following his release from Peterborough.
Source: BBC Sport
Source: BBC Sport