The senior UK Government minister on Monday avoided answering the question directly when pushed for a direction twice in a briefing to journalists.
Asked if he was expressly ruling out supreme court action in the event First Minister Nicola Sturgeon tried to hold a referendum, Mr Gove declined to do so.
He said: “I’m not getting into the whole question of courts and litigation and all the rest of it.
“If we start theorising in that area then we’re sucking oxygen out of the room when we should all be concentrating on recovery.
“Other people will, I’m sure, want to speculate or theorise about these questions, but to my mind every second spent asking questions about the Supreme Court is a second wasted when it comes to concentrating on the issues at hand.
"I mentioned I think light heartedly on the TV yesterday that I did if I walked down Sauchiehall Street that I doubted anyone would raise the urgency of Supreme Court action or indeed the need for independence referendum.
“I did do some shopping on Sauchiehall Street yesterday and I have to say it wasn't raised.”
Asked once again to directly rule it out, Mr Gove insisted he was “not thinking about it”.
He said: “I'm not going there. We're concentrating on recovery in the NHS, recovery in the economy, recovery in education, and recovery in the criminal justice system. That is our focus.“
Mr Gove also suggested voters who backed the First Minister were not necessarily doing so because of independence.
He said: “My interpretation of the election campaign in Scotland was that the First Minister put an emphasis, and I think she was right to do so, on Covid recovery.
“I also think it was also noteworthy that in a constituency vote more constituencies voted for union parties overall.”
Ms Sturgeon on Sunday warned it would be “completely outrageous” for the UK to block a second referendum after her party’s election landslide.
The First Minister was also asked on Sunday if the legislation for a referendum could be put before the Scottish Parliament early next year and said she would not “rule that out”.