Michael Clarke has been included in the party, but the Australia skipper is a doubt for the match after injuring his hamstring while batting as the hosts wrapped up victory in the first Test.
Khawaja, who played six Tests for Australia before being dropped after the series against New Zealand last year, has come into the squad as a potential replacement for Clarke.
With Ben Hilfenhaus also ruled out with a side injury, the national selection panel has turned to Mitchell Johnson and Bird as potential replacements.
Johnson was 12th man for the first Test victory over Sri Lanka and was considered unlucky not to be in the team after impressing at times during the third Test against South Africa in Perth, taking six for 164.
However, the paceman has struggled to take wickets at the MCG, having only claimed 13 scalps at the venue in four Tests.
Tasmanian strike bowler Bird, on the other hand, is regarded as something of an MCG specialist, having claimed an incredible 11 for 95 in a Sheffield Shield match last season.
Those figures came as Bird took 53 Sheffield Shield wickets at 16 in his debut year, before claiming 27 victims at 20.55 this summer to again sit top of the Shield wicket list.