The phrase "allow little time" is correct and usable in written English.
It can be used when indicating that there is a limited amount of time available for a task or activity.
Example: "Due to unforeseen circumstances, we can only allow little time for the presentation preparation."
Alternatives: "permit minimal time" or "grant limited time".
Short competitions allow little time for architects, clients or jurors to educate themselves in subjects that should form the basis for informed judgment.
These events will allow little time to dwell much on an era that came to an end three years ago, when the center was closed for this ambitious $75 million, 25,000-square-foot reconstruction.
But modern life can allow little time to maintain meaningful relationships, so what's the optimum number of friends?
A potentially new pandemic influenza virus, and particularly a highly pathogenic strain of a novel subtype, will likely allow little time for the development and production of a traditional strain-specific vaccine.
These factors allow little time for instituting the isolation and quarantine interventions that were essential in controlling SARS.
The high student-to-faculty ratios allow little time for individualized instruction and faculty guidance for those students who are unprepared for university-level science courses.
But his schedule, he said, allowed little time for friends.
He is quick-witted and allows little time to pass between one-liners.
Those who knew the young Roethlisberger described him as a person who was intensely driven to succeed in athletics but who was allowed little time to develop socially.
They were formally issued in June and approved Thursday, allowing little time for the clinics to meet requirements they described as unnecessarily onerous.
Adeeb's lawyers said the court had barred them from speaking on the fairness of the trial even though they were allowed little time to prepare their defence.
