Mr Burnham, who has expressed his anger at the decision by the First Minister announced last Friday, also disclosed he’d had more than 50 emails to his office about the “significant impact” on people lives.
He said the contacts included one individual due to marry at Gretna Green next month who had been forced to cancel and was unable to get the £500 deposit back, and a group of walkers who were double jabbed and are already in Scotland and "don’t know what they should do”. A family due to visit Scotland to scatter the ashes of a loved one had also been forced to cancel.
One hotel has also, he said, reported the loss of 200 room nights, “cancelled as a result of this”.
"So the impact is real,” Mr Burnham said.
"I anticipate having the opportunity to discuss it with the First Minister tomorrow and we will want clarity on elements of the policy which are unclear to us, the criteria and the exit strategy, but also how we might strengthen communications going forward.”
Mr Burnham was speaking at his Covid briefing as the Scottish Government said it would not compensate people and businesses from Manchester.
Covid recovery secretary John Swinney told MSPs they would not acquiesce to Mr Burnham's demands for compensation.
Mr Swinney said: "The government does not believe that would be appropriate.
"Travel to the north west of England has previously been prohibited last year, before local levels regulations were introduced and no compensation was offered.
“We are all responsible for putting in place, in our respective parts of the United Kingdom, the financial support to arrangements for business and that's exactly what the government will continue to do here in Scotland.”
Mr Burnham avoided the question of compensation at his briefing, saying he wanted to find a “resolution and clarity” over the ban.
It is understood he has been invited onto a four-nations Covid call where he will raise his issues directly with Ms Sturgeon.
"We are disappointed that people can’t visit – it has a real impact,” he said.
"I’m not going to contradict the position of the Scottish Government, but we are raising concerns about the policy, its implementation and lack of prior notice.
“It hasn’t been explained to us, so we’re not in a position to give people clear messages because we don’t know the rationale for this. Hence it’s a difficult position we find ourselves in. There has still been no contact with the Scottish Government directly, but I’m hoping to discuss these issues tomorrow.
“I’m seeking resolution, and a better way of doing things. It has been the case there have been restrictions with Wales, but the difference is this came in at very, very short notice and wasn’t communicated.
"And there’s a sense of inconsistency. Bolton has 250 cases per 100,000 and falling compared to Dundee, which is over 300, so when does the ban get lifted?”
Asked if he was using the issue to position himself in a Labour leadership challenge, as has been suggested by Ms Sturgeon, Mr Burnham said it was “unfair” to brand asking questions of the Scottish Government as an “ulterior political strategy".
“I think I find it disappointing that issues of substance are just dismissed in that way, as it suggests what we’re saying isn’t valuable and is manufactured, and I don't think you can say that because it’s having a real impact on people’s lives as I’ve described,” he said.
"It’s unfortunate that allegation gets made as it seeks to diminish the issues raised, which need to be properly considered.
"We have our differences with the UK Government, but they have generally got in touch with us to discuss what they were planning to do beforehand and when they have tried to put us under restrictions without support we have said that’s not right and the same applies to the Scottish Government.
“It does raise constitutional issues and are the legal grounds really clear? This is an unprecedented situation.
"It’s not just like a country saying these are arrangements for our country. The difference here is it impacts a particular area outside Scotland, it’s almost legislating for England. These things need to be considered.”
He added: “I’m not seeking to work against what the Scottish Government seeks to do to protect health, but we all of us have to work in partnership, especially when the decisions of one devolved administration impact on another. We need to find better ways of working.”
Despite a threat of legal action on Monday, Mr Burnham said that he would rather pursue a “political route”.
“That’s what we will do tomorrow, but to have a travel ban imposed by the Scottish Government when parts of Scotland with higher rates are not under similar arrangements, we are entitled to ask why,” he said. “We need a better resolution than the one we have now."
The Deputy Mayor of Policing, Beverley Hughes, said she had spoken with Greater Manchester Police about enforcement of the ban.
“We touched base on this question with the Chief Constable at the Covid committee meeting and as we anticipated he’s got no remit, he’s got no leverage, it’s impossible for him to police this issue even if he wanted to,” she said.
"What do we do – have a border around Greater Manchester and ask people where they’re going? It’s practically impossible for us to enforce.
"He’s also had contact with colleagues in Police Scotland and they to are feeling it’s very difficult for them to enforce in Scotland as well.”