Tower Hamlets, East London, GP Dr Sam Everington, who is BMA deputy chairman, will also be in the running.
BMA chairman James Johnson resigned on Sunday after losing the confidence of BMA members over a letter he wrote to The Times last week opposing the complete scrapping of the Medical Training Application System.
The new chairman will be elected at the BMA's annual representatives meeting next month in Torquay, Devon.
It is traditional for consultants and GPs to take turns chairing the BMA and, because Mr Johnson is a surgeon, it is likely that a GP will replace him.
Dr Meldrum was unavailable for comment.
GPC deputy chairman Dr Laurence Buckman confirmed that Dr Meldrum would be unable to continue as GPC chairman if elected to chair the BMA.
Dr Everington was also unavailable for comment.
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