The government insists it is still working towards early July as the possible date for the re-opening of pubs and restaurants in England.
Comments from a Number 10 spokesman downplay reports ministers could bring forward plans to allow the sector to start serving customers outdoors.
"The roadmap envisaged" an easing from 4 July and "we continue to follow the road map," Downing Street said.
The Financial Times reported that some ministers wanted an earlier start.
The government wants cafes, bars and restaurants to open as soon as possible, but it must be safe to do so, Number 10 said.
The Cabinet is expected to discuss progress towards easing the lockdown for the hospitality sector on Tuesday. Ministers have been working with a taskforce to assess the best way forward.
Business Secretary Alok Sharma warned Prime Minister Boris Johnson that 3.5 million jobs are at risk in the hospitality sector because of the coronavirus lockdown, according to the Sunday Times.
The pub and restaurant sector said that while easing restrictions earlier than July would be welcome, it would have made only a marginal difference.
Pub chain Wetherspoons said it would be a "psychological boost", while the trade body UK Hospitality said what was more important was whether the government would reduce the two-metre rule on social distancing to one metre.
As part of re-opening the sector, pubs, restaurants and cafes would first be able to serve customers in gardens, terraces, marquees, and similar outdoors areas.
But it comes amid growing concern about whether the government is easing the lockdown too early, risking a resurgence of infections.
Tim Martin, founder and chairman of Wetherspoon, said: "Few pubs will be able to make a profit using outdoor space only."
However, he said it would be a "psychological boost to a beleaguered industry", adding: "It will signal the intent of the government to make progress towards normality."
Kate Nicholls, chief executive of UK Hospitality, said that re-opening sooner would be welcome, but she questioned if two weeks would make much difference to a sector that has been in deep freeze for weeks.
"Businesses are still working towards 4 July... This gives some certainty about direction of travel. Some businesses have not opened since last November, because they are seasonal. It is important to start as soon as they can."
But re-opening could not be done overnight, she said. Businesses had to re-stock and bring back staff from furlough, for example. "It takes time, so the fact that there are talks about a specific date is helpful."
However, more helpful would be a relaxation of the two-metre separation rule, something pubs and restaurants say could be impossible to police.
According to the Financial Times, ministers have spoken to counterparts in Denmark about the success of that country's one-metre rules.
UK Hospitality has estimated that, with a two-metre rule, outlets would be able to make about 30% of normal revenues, whereas one-metre would mean about 60-75%.
Ms Nicholls pointed out that for many outlets, especially those in cities, the only outdoor spaces were pavements.
And she emphasised that just being able to serve customers outdoors would not be enough to save the sector from closures and job losses. Without tourists or the usual supply of customers from offices and shops, many pubs and restaurants would not survive, she said.