Mr Burnham, who has written to First Minister Nicola Sturgeon questioning the rationale for her decision, said he would be considering if legal redress was an option after compensation was ruled out by the Scottish Government.
He also raised questions about the enforcement of a travel ban, but stopped short of encouraging people from the north west of England to ignore Ms Sturgeon’s decision.
“I don't want to work directly against a legitimately democratically elected government, but I am struggling very much to see how this is proportionate or justifiable,” he said.
"To ban double jabbed, older people, from the entirety of Scotland … I think that’s an infringement on their civil liberties, definitely.
“Just to say that you cannot go to Scotland because you happen to live in Salford, Manchester or Bolton, when all the evidence that we have locally is that the cases are significantly within the under-25s, the case rate amongst the over-60s is very low. I think it is an infringement of their civil liberties.
"I'm not going to directly contravene another democratically elected devolved administration by telling everyone here to ignore them. But at the same time, I'm struggling to understand their policy.”
He added: “I also don’t know how the ban gets enforced, to be honest. That is also a matter for the Scottish Government to set out.”
Mr Burnham said there was a lack of “consistency and fairness” in Ms Sturgeon’s decision. “I cannot understand at all, how tonight, Bolton is under a Scottish Government travel ban because their cases are below 300 and falling,” he said.
The mayor said he had received emails from Bolton residents about the damage of the travel ban and that “dismissing” compensation, as Deputy First Minister John Swinney did earlier on Monday, was not acceptable.
"What does the Deputy First Minister say to a couple from Bolton who've been in touch with me today who are over £1,000 out of pocket, because their holiday cottage in the Borders has been cancelled this week with no ability to get a refund?" Mr Burnham asked.
Asked if he would consider legal action, he added: “I certainly think there is some shaky ground here for the Scottish Government.
"I don't know if they could demonstrate fairness across the different areas affected by restrictions. It raises the question of discriminatory action against people living in some areas.
"So I've had actually a lawyer getting in touch to offer help. I'm not necessarily saying that to say that we're going there.
"Threatening legal action is something that only should be done if appropriate, but I can't rule out. If there's hundreds of people that are out of pocket by hundreds of pounds ... if there is a legal redress route for them, then I think that should be considered.”
A spokesperson for the First Minister said there was nothing further to add to Ms Sturgeon’s comments from earlier on Monday when she said the measures were taken for public health safety.