Sunderland striker Andrew Nelson spent the second half of last season on loan at Falkirk.
Scott Bain, who joined Brendan Rodgers’s Celtic on loan from Dundee in the January transfer window, has previously worked with Falkirk manager Paul Hartley.
The 6ft 6in shot stopper will join up with the Bairns for the rest of the season.
Rangers summer signing Ryan Jack and former Celtic midfielder Paul Hartley played together at Aberdeen.
Dundee manager Paul Hartley speaks highly of Celtic midfielder Scott Brown.
Mark Warburton's Rangers side play host to Dundee at Ibrox tomorrow.
The Celtic captain has been in fine form at the beginning of this season.
Paul Hartley says he will not sell anyone this summer.
The Dundee striker has been linked with Leeds United, Aston Villa, Queens Park Rangers, Derby County and Bolton Wanderers.
Dundee FC manager Paul Hartley reveals he wants to keep hold of Leeds United target Greg Stewart.
Remi Garde has lost his job as Aston Villa manager - who could replace him?