Chelsea had sold between 500 and 600 tickets of their 4,620 allocation before the licence placing restrictions on the club came into effect on 10 March.

The measure was introduced to stop oligarch Abramovich, who is looking to sell Chelsea, from profiting.

He has been banned from being a club director and the sale of Chelsea has been delayed after the UK government sanctioned him over his connection to Russian President Vladimir Putin.

Chelsea said they made the request to the FA to play Saturday’s game behind closed doors “with extreme reluctance”, saying they had done so “for matters of sporting integrity”.

A statement read: “Chelsea FC recognises that such an outcome would have a huge impact on Middlesbrough and its supporters, as well as our own fans who have already bought the limited number of tickets that were sold before the licence was imposed, but we believe this is the fairest way of proceeding in the current circumstances.”

Middlesbrough, who have knocked out Premier League sides Manchester United and Tottenham in this year’s competition, responded: “To suggest as a result that MFC and our fans should be penalised is not only grossly unfair but without any foundation.

“Given the reasons for these sanctions, for Chelsea to seek to invoke sporting ‘integrity’ as reason for the game being played behind closed doors is ironic in the extreme.”

Government in discussions over further ticket sales

Chelsea said on Monday they were talking to the government on a daily basis “in search of a resolution” to the issue of selling tickets, and that the Premier League and FA had spoken to the government about the potential sporting integrity issues raised.

The government last week granted an amendment to the licence, allowing Chelsea to spend £900,000 on costs for home games – up from the £500,000 set on Thursday.

However the allowable away costs remain at £20,000 per game.

Sports minister Nigel Huddleston said the government is in “discussions” with Chelsea “to look at ways ways we could potentially enable further ticket sales”.

Speaking at a Digital, Culture, Media and Sport (DCMS) session about the role of Russian money in the ownership and sponsorship of clubs, Huddleston said licence amendments taken so far were “precisely to stop” Chelsea from going into administration.

Travel needs are about injuries, not ‘bling’ – Tuchel

Chelsea manager Thomas Tuchel, whose side face Lille in the Champions League last 16 second leg on Wednesday, said they have made adjustments to travel with a budget of £20,000.

The amount spent on travel for an away Premier League match is about £30,000, while European away fixtures add an extra premium.

Tuchel said travel needs were centred around players avoiding possible soft-tissue injuries during a busy schedule rather than “luxury and bling bling”.

“This is just a professional level of sports, where we play with two days between matches with our opponent having four days between matches and we arrive with the possibilities of injuries,” he said. “For that, it is better to arrive with a plane rather than a bus.”

“From my understanding, we have a framework to go and play in Lille with absolutely no excuses.

“Regarding these organisations, it is already more difficult to arrange things on a professional level, in the best way possible, for the FA Cup.

“But we will deal with it. As long as we have shirts and are ‘alive’ as a team, we will be competitive and fight hard for our success. We owe it to the people who support us.

“We are in the spotlight and it is our responsibility to do so. We will do it.”

Chelsea’s FA Cup quarter-final against Middlesbrough, which starts at 17:15 GMT on Saturday, will be broadcast live on BBC One, BBC iPlayer and the BBC Sport website.

‘Blues could be millions out of pocket’

BBC Sport’s Simon Stone

BBC Sport has been told Chelsea never thought it was likely the Football Association would agree to their request.

However, it was done to try to get the government to understand the complexities around the predicament they are in.

Under FA rules, Chelsea are entitled to 45% of the gate receipts from Saturday’s game. In theory, that should net the Blues in excess of £300,000.

But they have no idea whether they will receive the payment – or whether it will be withheld within the terms of the special licence, handed out by the government, which they are operating under.

In April, they have home games against Brentford and West Ham – and could also have a Champions League quarter-final and FA Cup semi-final to play. If Chelsea are not allowed to sell tickets, they will be millions of pounds out of pocket which could have a massively damaging impact on the club.