Political leaders in the region have so far refused to accept the highest level of restrictions without greater financial support for businesses and residents.
Boris Johnson on Friday urged Mr Burnham to work with the Government but also said he retained the right to unilaterally intervene if necessary.
"Let's remember, the places they're trying to close in tier three - pubs, bookies, gyms - these are places where people are on low wages".
'As more people get infected that will place more pressure on the NHS and the more people sadly in intensive care beds in the North West and in Manchester who are suffering from coronavirus, the fewer intensive care beds are there for people with other serious conditions.
'The nature of the epidemiology... is different in this wave than it was earlier in the year'.
Ms Patel also spoke to chief constables in Lancashire, Wales and Merseyside "to make sure they have all the support they need from national politicians but also, more importantly, from local politicians", said a Home Office source.
He added the government wanted the best for Greater Manchester and that he hoped "we can find a way through together".
But the mayor and council leaders across Greater Manchester responded by insisting they have done "everything within our power to protect the health of our residents". We've been under those restrictions for three months and people's mental health now is pretty low.
'This isn't about politics or about money, this is about people'.
The row over a possible Tier 3 lockdown in Manchester is continuing, with Mayor Andy Burnham blaming Chancellor Rishi Sunak for being "the problem" amid confusion over talks with Downing Street. And the number of people in hospital has risen sharply since last week.