Australian international Johnson, 30 last month, is a combative midfielder who also worked with Jackett at Watford.
Former Manchester City star Edghill, 29, is a vastly experienced full-back - he made more than 200 appearances in his Maine Road days - who can operate on either side of defence.
And veteran Palmer, QPR's club captain this season, is a central defender or midfielder who played under Jackett at Watford before following him to West London in 2001.
Rangers striker Paul Furlong - once a £2.3million signing for Chelsea - is another Watford old boy mentioned as a possible target, though he may be offered a new deal at Loftus Road.
Jackett is also thought to be keen on striker Paul Tait, who is out of contract at Bristol Rovers.
The 29-year-old Geordie has also had spells at Wigan, Crewe and Hull since leaving Everton as a youngster.
Neil Cutler remains favourite to take over as Swansea's first-choice goalkeeper next season despite being offered a new contract at First Division Stoke.
The 27-year-old, who played 13 games during a loan spell at the Vetch a year ago, has expressed an interest in returning as he searches for regular first-team football.
Current Swansea No. 1 Roger Freestone was one of eight out-of-contract players today waiting to discover if they will be required next season.
Also on the endangered list were Michael Howard, Kris O'Leary, Jon Coates, Kevin Nugent, Stuart Roberts, Stuart Jones and Matthew Rees.
Of those it is thought only two or three will be offered new terms, while Jackett is also likely to show the door to some of those players under contract beyond this summer.
He has already told Karl Connolly, Richard Jones, Layton Maxwell and Lee Fieldwick that they can go as he makes room for as many as 10 summer signings.