Prime Minister David Cameron will head to Brussels next month to try to finalise renegotiations of Britain's relationship with the EU before putting the deal to the country in a referendum before the end of 2017.
Lord Rose said he hoped Mr Cameron would secure a deal in February allowing an early referendum - which some observers believe could come as soon as June.
Speaking to LBC radio, the Stronger In chairman recognised that migration was "the issue of our time", but added: "I don't want this referendum to be totally dominated by the migrant crisis."
He called on Eurosceptics to set out evidence on what future trade deals would look like outside the EU, arguing that everything from food to clothing, travel and insurance would be more expensive if the UK left.
Britain Stronger In Europe is highlighting research by the Centre for European Reform that found Britain's goods trade with the EU is 55% higher as a result of its membership.
The "EU effect" was worth around £133 billion to the 200,000 export and import companies in the UK in 2014, it said.
"I am pro-Europe in the sense that I would absolutely be in Europe, with its imperfections, rather than risk being out with the unknown."
Lord Rose
Lord Rose told LBC: "The EU is not perfect. I have always been a bit of a Eurosceptic. But, I say to myself, it is the reality of what we have got today versus the risk of tomorrow. What we don't know is what is the risk?
"We are not in the euro, we are not in the Schengen agreement, we haven't got open borders, we have got some protections, we are not going to go into the euro and we do get massive benefits form being in the EU.
"We have got £350-odd a year the cost of us being in, per person, and £3,000 a year the benefits - calculated independently - of being in. That's a 10-to-one return. Do we want to sacrifice that?
"I am pro-Europe in the sense that I would absolutely be in Europe, with its imperfections, rather than risk being out with the unknown."
Lord Rose said World Trade Organisation rules would inevitably mean higher taxes on trade with European neighbours if Britain left.
Vote Leave highlighted the Civitas reported which analysed trade statistics and found Britain's membership of the EU has failed to have a significant impact on export growth.
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Academic Michael Burrage, who wrote the report, found the bloc has boosted the exports of non-EU countries more than its members, with Britain recording slower export growth than any of the other founding nations.
Growth of exports between member states during the common market was 4.7% but has fallen to 3% in the single market, the research said. UK export growth fell from 5.38% to 3.09% over that period.
Exports between the 12 founding members of the single market are 14.6% lower than if they had continued to grow between 1993 and 2012 as they had done under the common market, the report adds.
Mr Burrage said: "While the single market cannot be counted a success in export terms for the EU as a whole, for the UK it must be counted at the very least a massive disappointment, and not far short of a disaster."
Vote Leave chief executive Matthew Elliott said: "The unquestioning mantra that the single market has been good for British trade is wrong and should be challenged as this research makes crystal clear."
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