Mr Alexander said Britain's national interest had to trump party political difficulties.
"I just think that any responsible British politician should not be contemplating British exit from the EU given how serious the consequences should be," he said.
"Of course there are difficulties on Europe in different political parties," he told Sky News' Murnaghan programme. "But in the end it is our national interest, our national interest in terms of our economy and jobs and society that has to come first in any approach."
Earlier this week George Osborne issued an ultimatum to the European Union, saying it “must change” in order to avoid a British exit.
“I very much hope that Britain remains a member of the EU,” the Chancellor told Germany's Die Welt . “But in order that we can remain in the European Union, the EU must change.”
“David Cameron has said recently that a new consensus is necessary for our relations with Europe,” Mr Osborne is reported to have told the newspaper, adding that the British people are currently “very disappointed” with the EU.
Mr Alexander this morning told the broadcaster: "It was Margaret Thatcher who led the foundation of the European single market which is very important to British business and British jobs.
"That is why we have seen a lot of business leaders over the last last few days coming out very strongly and saying they want to see Britain's place in the EU maintained."
Mr Alexander said there were "many reasons why Britain is an attractive place to invest".
"But it is clear that for many sectors for many investors our place in the European single market, our participation as a leading member of the EU is part of that mix," he added.
He insisted Mr Cameron had been "very clear he does not want Britain to leave the EU".
Earlier Ed Miliband ruled out a referendum on Britain’s membership of the European Union.
The Labour leader said David Cameron’s position on Europe is “incredibly dangerous” and that the Prime Minister is “sleepwalking us towards the exit door”.
Mr Miliband said that promising an in/out referendum on the UK's position in the EU is the “last thing we should do”.
”It’s the wrong thing to do,” he said on the BBC's Andrew Marr Show. “It is not in the national interest."
The Prime Minister will this month give a major speech about Britain’s future in Europe, which could pave the way for a referendum on EU membership.
Some Conservatives say Britain should leave the EU if other members do not agree to much looser membership.
Mr Cameron has promised to seek a “new settlement” for Britain in Europe, then put the deal to voters for their consent.
"I think that it’s incredibly dangerous what David Cameron’s doing,” Mr Milliband said on the programme, which was presented by James Landale after Mr Marr suffered a stroke.
“I think he is essentially sleepwalking us towards the exit door from the European Union.
“The last thing we should do is start to say for some date five, six , seven years hence, let’s decide now to have an in/out referendum.”
Although Mr Miliband failed to guarantee that he would not consider a referendum after the 2015 election, he said he believes it would be a “bad idea”.
He said that Mr Cameron is only making the pledge to negotiate a new settlement for the UK in Europe because of the threat from Ukip as well as unrest among Conservative backbenchers.
“We know why this is happening,” Mr Miliband said. “He’s worried about the threat from Ukip and he’s worried about what’s happening in his own party.
“It’s the wrong thing to do, it’s not in the national interest.”
“But I’m very clear, the question for now is should we have a referendum? Should we commit to a referendum? Should we promise one? And I’m saying very clearly to you, no is the answer.
“I’ll set out at the election what our position is on the issue. I’m not going to speculate about years hence but I’m giving you a very clear view that it’s the wrong thing to do.”
A poll has shown that Mr Cameron could slash Ukip's support by more than a third if he promises an in-out referendum on EU membership
Research by ComRes for the Sunday People found 63% of the public want a vote on whether Britain should remain in the union.
Some 33% said they would cast their ballot in favour of a full withdrawal – including two thirds of Ukip supporters, 27% of Tories, 25% of Labour voters, and 17% of Liberal Democrats.
However, more people – 42% said they were against leaving the EU.
There were also signs that opposition to the union has softened, with the proportion who think there should be a referendum dropping from 68% in October 2011.
At that time 37% wanted to exit the EU altogether.