Communities Secretary James Brokenshire said there might more non-binding votes on Brexit alternatives instead.
May will make a statement to parliament on February 13 updating lawmakers on her progress so far in seeking changes to her deal.
Labour leader Jeremy Corbyn, who has written to the prime minister setting out his demands for a Brexit deal he could support, accused May of an "utterly cynical" approach.
The government has not ruled out supporting this - and has promised a formal response to it and further talks with Labour - but they say it would prevent the United Kingdom from making its own trade deals after Brexit.
The Prime Minister has been in Brussels this week seeking concessions on the Northern Irish backstop, the reason many MPs rejected her vote by historic margins in January.
British Prime Minister Theresa May has rejected the idea of targeting a customs union with the European Union, pouring cold water on hopes from some that she could shift her Brexit policy to win over the opposition Labour Party.
In the vote this week lawmakers are set to vote on amendments that could limit May's options and give parliament a broader say over the Brexit process.
In the interview Starmer described Mrs May's approach as "reckless" and "blinkered" and blamed her "tunnel vision" for the devastating defeat suffered last month when MPs threw out her Brexit deal by a record 230 votes.
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She has said she wants to bring a revised deal back to parliament for a vote "as soon as possible" but has not yet set a date for doing so.
Sir Keir earlier said his plan was necessary to put a "hard stop" to Mrs May "running down the clock" before the March 29 deadline.
If May succeeds in winning changes to her Brexit deal in the next few days she could bring it back for a debate and vote before February 14, and this more general debate would not go ahead.
May's Brexit minister Stephen Barkley will meet European Union negotiator Michel Barnier on Monday and foreign minister Jeremy Hunt will visit Paris and Warsaw this week.
May held talks in Brussels last week in an attempt to secure changes to the Northern Ireland backstop as demanded by Tory MPs.
A number of government ministers will also be meeting their counterparts across the continent this week, in order to underline Mrs May's determination to achieve a deal.
Tony Blair has echoed warnings that a no-deal Brexit would lead to "potentially devastating" consequences to the peace process in Northern Ireland.
The Government is stepping up efforts to persuade the European Union to accept changes to the Irish border backstop in the Withdrawal Agreement.