He was last at Dundee United, having a spell on loan in England with Gillingham prior to his Tannadice release over the summer.
The report claims he is only training with the Bairns for fitness, with a move not on the cards anytime soon.
King would be decent for Falkirk
It would be another high profile capture if Falkirk did manage to get a deal done for King. They already have former Premiership players like Connor Sammon, Morgaro Gomis, Ian McShane and Lewis Longridge.
King’s a decent enough player but he struggled for form over his United spell. Overall he made 66 appearances for the Tangerines, scoring ten and assisting on 13 occasions.
He’s never been able to emulate his Hearts form, which managed to convince Rangers to sign him. Whilst in Gorgie, he scored 16 times and notched 25 assists over 96 appearances.
Rangers didn’t work out for him though and he’s struggled every since. In League One though, King has enough experience that would make him a great player at third tier level.
A deal doesn’t seem to be forthcoming though, as the former Hearts and Rangers man waits for another club.