The Observer reported last night that a senior civil servant at the Department for Education (DfE) had been paid off after a grievance procedure involving Gove's special advisers.
But Gove, asked at a Commons select committee hearing whether he was aware of inappropriate behaviour by his special advisers, answered: "No... I am not omniscient but I have seen no evidence of that."
Shadow education secretary Stephen Twigg said Gove faced "incredibly serious allegations".
He said: "It appears that Michael Gove has either misled Parliament or appears to have no control or knowledge of what his advisers do on his behalf.
"Misleading Parliament would be a breach of the ministerial code. We need a full investigation by the Cabinet Secretary."
A DfE spokeswoman said: "It would not be appropriate to comment on individual employment matters."
There were also claims last night that Gove was planning to privatise academies and free schools.
The Independent on Sunday said a memo drawn up by the department showed the Education Secretary was looking at "reclassifying academies to the private sector".
The Liberal Democrats had not been informed of the idea, the paper claimed.
Chris Keates, general secretary of the NASUWT union, said: "Since the Secretary of State's academisation programme began, we have maintained that the agenda was to put as many schools as possible into predatory chains of private providers.
"Instead of the focus at the DfE being to discuss how to support children and young people and the school workforce, everything is dominated by this obsessive focus on structural change which does not raise standards, and how to turn a fast buck at the expense of the taxpayer.
"Education is in the grip of a free marketeer who knows the price of everything and the value of nothing."
The DfE said: "There is no plan to allow schools to make a profit."