The UK Government's Education Secretary, a former pupil at Robert Gordon's College in Aberdeen, denied allegations he was trying to politicise Ofsted and said Baroness Morgan's replacement would be appointed "on merit".
The Labour peer, who used to work for Tony Blair, claims she is the victim of a "determined effort from No 10" to appoint more Tories.
Schools Minister David Laws, Mr Gove's Liberal Democrat deputy, is said to be "absolutely furious" at what he sees as a blatant attempt to "politicise" Ofsted.
A source close to Mr Laws said: "The decision to get rid of Sally Morgan had absolutely nothing to do with her abilities, or even education policy, and everything to do with Michael Gove's desire to get his own people on board."
The Secretary of State said Lady Morgan, whom he appointed, had done a "fantastic job" but stressed that "from time to time you need to refresh the person in charge". He pointed out how a former Labour special advisor had been taken on to head the NHS.
Asked if Tory donor Theodore Agnew, an insurance magnate who worked closely with Mr Gove before the last general election, was lined up to succeed Lady Morgan, the Education Secretary did not comment, stressing again the Ofsted appointment would be made on merit and it would be "quite wrong" to rule out a suitable candidate "on the basis of their political allegiance".
Later, Sir Malcolm Bruce, the new deputy leader of the LibDems, claimed Mr Laws had not been properly consulted over Lady Morgan's planned axing.
Asked if his party was simply picking a fight with the Tories to create some clear water ahead of the General Election, Sir Malcolm replied: "Michael Gove is picking a fight here. We know he has a very definite ideological position; he comes from a private school background himself. That's what he wants to drive."