The offer to Ms Lemmie, a city manager in Dayton, Ohio, was withdrawn after extensive speculation on both sides of the Atlantic about whether or not she would actually take up the job.
'For a variety of personal reasons she is not able to leave the US and move to England,' a senior council source said. 'So we are withdrawing the offer rather than waiting around.'
At present the council is not sure what its next move should be.
Sheffield City Council chief executive Bob Kerslake and Sunderland City Council chief executive Colin Sinclair were on the shortlist with two other international candidates.
Mr Kerslake said it was unlikely he would take the job if offered.
'I applied because Birmingham is considered the top job in local government, but there was no push factor for me here at Sheffield. I am quite happy here,' he said.
'My feeling is that Birmingham would probably want to go through the process again. Given the importance of the job it wouldn't be appropriate to just take someone else on the list.'
The withdrawal is the culmination of a week of speculation about the appointment, announced by the council last week.
Political leaders in Dayton, Ohio, were shocked when they heard of the appointment and said they would make her a counter offer.
Shortly afterwards Ms Lemmie issued a statement saying she had not signed a formal contract with Birmingham and was leaving her options open.
There has been speculation Ms Lemmie was unhappy with the 40% tax she would have to pay, or that she may be holding out for a better offer in Dayton.
But the Birmingham source said Ms Lemmie had personal reasons for pulling out of the agreement.