The 34-year-old spent six years at Millwall as a player before moving to QPR, where he is now a youth-team coach.
Jackett resigned as manager just three days after the season ended having guided the club to Championship survival.
Bircham is as short as 4/7 to be named the next permanent boss, while Gary Johnson, Neil Warnock and Andy Hessenthaler are also in the reckoning.
The ex-Canada international hung up his playing boots in 2009 after a long fight against a succession of back, hamstring and ankle injuries.
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