Douglas Ross, party deputy for Moray, said he could not support any agreement that includes staying in the PPC beyond the current departure date of 2020.
This week raised concerns about the possibility that the UK will remain part of the political controversy beyond this date, after the Prime Minister indicated that the transition period could be extended to ensure a Brexit agreement.
Speaking about the BBC's Sunday Politics Scotland, Ross said: "I could not support an agreement that would include remaining in the Common Fisheries Policy beyond December 2020."
He said that an extension of even three months would be too long.
When asked if there was unanimity among the Scottish Conservative deputies for this opinion, he said he understood that they could not support such an agreement.
If the 13 deputies of the party vote against the Brexit agreement, the government would lose the majority of the House of Commons.
Mr. Ross added: "I think the important thing is that we send a very strong signal to all those who are negotiating on behalf of the United Kingdom that this is an issue that is extremely important for our Scottish communities that we represent.
"My opinion is that it will not come to that (a difficult Brexit instead of staying in the CFP).
"You will see that there is a very clear and distinct message from the Scottish conservatives, and indeed from Scotland, that we can not have the CFP."
The leader of SNP Westminster, Ian Blackford, told the same program: "What Douglas Ross and the conservatives must recognize is that they are threatening a difficult Brexit."