The pair were both injured in last Saturday's Champions Cup defeat to Northampton and join an already extensive list of back rowers currently unavailable for selection.
Allen sustained what has been described by Medical Performance Manager, Chris Towers, as "significant ligament damage" while Bearman suffered a groin tendon injury.
Both players have undergone scans to reveal the extent of their injuries and will meet with specialists later this week to discuss treatment, but Towers confirmed that both are looking at lengthy spells on the sidelines.
While Dan Baker and James King are on international duty with Wales, the Ospreys are already without Tyler Ardron and Olly Cracknell (both ankle) and Tom Smith (knee) so have looked to find extra cover from outside of the squad.
Andrew Millward, Rugby General Manager, said:
"To lose Morgan and Joe on Saturday night means that with Dan on international duty we are without our three front line number eights. Add into the mix James being with Wales and the other back rowers who are currently injured and we are clearly light on numbers going into a very important month of rugby with some very tough fixtures ahead.
"Because of that, we've had no option other than to bring in someone on loan and are grateful to the Blues for allowing Ieuan to join us for a month. He's a ball carrier with considerable experience for his age and we are looking forward to seeing him taking this opportunity and making an impact in an Ospreys shirt."
21-year old Jones, from Aberbargoed made 32 appearances (five tries) for Newport Gwent Dragons before moving to the Blues in the summer, where he is yet to make his debut.
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