A Scottish Parliament spokesman said a full statement would be made by Mr Finnie on 8 January.
Scottish Tory fishing spokesman Jamie McGrigor said that the decision reached in Brussels "need not be the last word".
"Such significant changes to the management of fishing stocks cannot, under EU rules, be implemented unless debated by the full European Parliament," he said.
"My colleague Struan Stevenson is pressing for this and will, if necessary, take the commissioner to court."
'Realistic future'
He said there should be a return to national control of fish stocks and fishing waters.
Meanwhile, the Church of Scotland has said it will do all it can at a grassroots level to help fishing communities.
The convener of the Kirk's church and nation committee has urged Mr McConnell to secure a "realistic and hopeful" future for Scotland's fishing communities.
The Rev Alan McDonald said that support and aid needed to be as generous as possible.
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