Michael Gove has said he has seen "no evidence" of inappropriate behaviour by his special advisers, reports the Observer.
Shadow education secretary Stephen Twigg said Mr 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."