The sausage-maker said sterling's weakness following the Brexit vote was making the cost of British pork more competitive internationally and cheaper for UK retailers than EU imports.
British pig meat had been 10p per kilo more expensive than the average EU price, but since the Brexit vote it has become 10p-15p cheaper.
Chief executive Adam Couch told the Press Association: "In the long term, there's certainly an opportunity. If the pound remains weak then the UK will look very competitive."
But he said the UK imports around 50% of its pig meat and it would take a significant capital investment over a long period of time from British pork producers to start driving that number down.
The FTSE 250 firm saw its Asia exports grow 60% to £50m in the first quarter compared with last year, as it capitalised on China's appetite for pork and the country's dwindling domestic supply.
Couch said the post-referendum currency fall had reinforced its overseas contracts and had inspired some strong sales for the wider UK market.
Lizzie Wilson, policy services officer for the National Pig Association, expects UK pork producers to boost their profitability and output thanks to the favourable market conditions created by the Brexit vote.
"I imagine until Article 50 is triggered it seems like there will be a degree of uncertainty which will impact the exchange rate.
"If this continues for a number of months - and with import costs remaining quite low in terms of feed - it will create a degree of profitability (for UK pork producers) that could be invested into buildings and equipment to increase capacity."
She said this could help meet a rising demand from British retailers attracted to the competitive price of British pork.
"British retailers infinitely prefer British, provided it's the right price and they're able to source adequate supplies," she added.
Cranswick announced at the end of last month that revenues rose 11% in the first quarter to 30 June, as it boosted volumes to meet increasing demand from Asia.
The Hull-based company plans to expand volumes further by ploughing £47m of capital investment into its UK factories over this financial year.
It will include £7m of investment at its pork processing plant in Norfolk and £10m at its Benson Park poultry factory in Hull.
The firm sold its sandwich business at the end of July to Greencore in a £15m deal.
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