(CNN)Attorney General William Barr has warned Democrats on the House Judiciary Committee he won't show up to this week's highly anticipated hearing if they stick to the format the chairman has proposed for the questioning, according to a committee source with knowledge of the matter.

Skipping this week's hearing would amount to a dramatic escalation in the growing fight between the Trump administration and House Democrats over a range of oversight requests, including over access to the unredacted report from special counsel Robert Mueller, the subject of Thursday's hearing.

But it's still possible they could reach a deal by Thursday, meaning Barr might ultimately show.

The Department of Justice did not immediately comment