Fergus Ewing said as it was unclear who would form the next government at Westminster, the "pragmatic approach" would be for him to take charge in the key Brussels talks.
With European fishing quotas due to be negotiated in the next few weeks, Mr Ewing is to write to UK Environment Secretary Theresa Villiers to make his case.
With MPs at Westminster facing a General Election on December 12, Mr Ewing said there was "no certainty who will form the UK Government" and it was unclear which minister would lead the quota negotiations.
As a result, he added: "I do think it would make sense that Scotland should lead the negotiations on behalf of the UK, I hope the UK Government might agree such a sensible and pragmatic approach."
He insisted it would "benefit the whole of the UK" if he was to take charge of the negotiations.
Mr Ewing said: "In that spirit, I will write to the current Secretary of State Theresa Villiers offering so to do."
The Rural Economy told MSPs scientific advice on fishing quotas made for an "extremely challenging picture" for some parts of the industry, with a suggested 61% reduction in the catch for North Sea cod in 2020.
However, he added there was "more positive" news for some parts of the sector, with scientists favouring an increase in the amount of mackerel, blue whiting and North Sea herring that can be landed next year.
However, Tory MSP Peter Chapman insisted that leaving the European Union was the way to improve prosperity in Scotland's fishing communities.
"Surely not even the SNP can argue it is fair that 60% of the fish in our waters are caught by foreign boats," the Conservative said.
He claimed leaving the EU's Common Fisheries Policy (CFP) could see catches double and "could result in an increase of £500 million to the economy and 5,000 jobs".
Mr Chapman said: "We are the party who will take the UK out of the EU, we're the party that will take fishmen out of the Common Fisheries Policy.
"The SNP have nothing to say to our fishing communities in the North East, be in no doubt, the SNP's stated objective is to stop Brexit and rejoin the EU as quickly as possible and take us straight back into the CFP."
He continued: "We fully realise the great opportunity Brexit provides to the fishing industry by leaving the CFP.
"Access by the EU fleet to our waters will no longer be an automatic right as it is under the CFP, but something that will be subject to annual negotiations, as is currently the case for countries not bound by the CFP, such as Norway."