Elsom has recently shown his commitment to his homeland by resigning with the Australian Rugby Union but the ARU are yet to find him a Super 15 franchise for next season.
The 26-year-old has made it clear that he wants to leave current outfit the Brumbies but two of the other four franchises have stated that they won't be signing the Wallaby star.
Elsom had apparently been keen on a move to the Waratahs but they have admitted they can't afford to meet his financial demands without outside assistance.
And now the Reds have joined the Waratahs in seemingly pulling out of the race for Elsom's services.
''I did a lot of signings last year. So we have quite a few back-rowers on two-year deals and keeping hold of Beau Robinson is a priority for us," Reds boss Ewen McKenzie told the Sydney Morning Herald.
"So we've pretty much got no space. If we had this discussion in March, you might have a different discussion."
Of the two remaining Australian sides, newboys the Melbourne Rebels would seem the more likely option for Elsom who is not expected to make the trip to Perth to join the Western Force.
And while Elsom has pledged his future to the ARU, difficulties in finding him a franchise could soon lead to rumors that the former Leinster flanker could yet be tempted to look overseas once more.