Brexit: Assembly put on standby for recall if no-deal
The first minister will request the assembly be recalled from recess if a summit in Brussels later results in the the UK leaving the EU without a deal.
Writing to Presiding Officer Elin Jones, Mark Drakeford says such an outcome is "unlikely".
EU leaders will consider offering a further Brexit delay beyond the current exit date of this Friday.
Mr Drakeford suggests if there were a recall, AMs could sit on Thursday afternoon.
This would allow the Welsh cabinet to meet in the morning.
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The prime minister wants the new departure date to be 30 June but the EU is expected to offer a longer delay.
European Council President Donald Tusk has urged the other 27 leaders to back a flexible extension of up to a year - with conditions.
In his letter, sent on Tuesday, Mr Drakeford says: "As things stand today, we believe a no-deal outcome is unlikely, but the situation continues to be volatile and I will not be in a position to make a decision about whether to make a formal request to you until after the European Council tomorrow - late tomorrow [Wednesday] evening or first thing on Thursday morning.
"Until that point I believe it would be prudent to have contingency plans for recall in place.
"If I were to request recall, it would be to suggest the National Assembly meets on Thursday afternoon, giving members time to travel to Cardiff, and to enable the cabinet to meet in the morning."
The UK is currently due to leave the EU at 23:00 BST on Friday, 12 April, which was postponed from the previous date of 29 March.
If no extension is granted, the default position would be for the UK to leave on Friday without a deal.
So far, UK MPs have rejected the withdrawal agreement Mrs May reached with other European leaders last year.
But the Commons has also voted against leaving in a no-deal scenario.