The move is one step short of publicly declaring the constitution dead, an act for which no EU government wants to take the lead for fear of being blamed for its demise.
Straw is to address parliament at 3:15 pm (1415 GMT) on Monday. When the government announced its referendum plan late last year, it was clear the intention was to hold it in the first few months of 2006.
Political analysts say it is in effect the death knell for a charter that advocates argue is vital to streamline the 25-nation bloc's cumbersome bureaucracy but opponents say would move too much power to Brussels.
"I will be amazed if Straw doesn't explicitly or implicitly make it clear that Britain will not go ahead with the referendum plans," said Anthony King, professor of politics at Essex University.
"My guess is that he will signal - even if he doesn't say in as many words - that he and the British government regard the constitution as dead," he said after voters in France and the Netherlands - two of the EU's founder member states - threw the bloc into crisis by rejecting the charter in referendums last week.
Prime Minister Tony Blair, in power for a third and final term and keen to secure a legacy other than the unpopular Iraq war, has long declared an ambition to put Britain at the heart of Europe.
"But now that the French and the Dutch have said 'no', Tony Blair has got off a political hook because it would have been rejected by the British people"
Essex University professor
However, while ratification of the constitution could have been just the epitaph for which he is looking, deeply Eurosceptic Britons were unlikely to have done him the favour.
"I suspect that Blair would have liked the constitution to have been adopted by the whole of Europe. After all, the British government put a lot of effort into drafting it," King said.
"But now that the French and the Dutch have said 'no', Tony Blair has got off a political hook because it would have been rejected by the British people," he said
Ten EU countries, accounting for about half the bloc's population, have approved the constitution, but the rejections by French and Dutch voters have raised doubts about whether it remains viable.