The total more than doubles the target raised in memory of Albion supporter Rob Spray, aged 32, from Heath Hayes in Cannock.
Mr Spray died after being found in Sofia on Monday morning ahead of England's European Championship qualifying match.
The cause of death has not yet been confirmed but authorities say they are working to clarify the circumstances surrounding the incident.
But Mr Spray's family told reporters that they have appealed to the office of Cannock Chase MP Amanda Milling and the Foreign Office for help.
A liaison officer from Staffordshire Police is also working with the family to contact the Bulgarian authorities.
A Staffordshire Police spokesman said: “A family liaison officer from Staffordshire Police is supporting the relatives of a Cannock man who died in Sofia, Bulgaria.”
Mr Spray's sister Katie Brown told reporters Bulgarian police had yet to give the family any answers over his death.
She wrote on Facebook that "he died in police custody in suspicious circumstances".
His family say Mr Spray was a West Bromwich Albion season ticket supporter and fans have come together to pay tribute and share their condolences online.
More than £10,000 was donated within 12 hours of the gofundme page being set up by Mr Spray's friends Roger Wootton and Sam Tongue.
And now the fundraising total stands at more than £20,000 today.
Mr Wootton writing on the page today said: "We've smashed 20k which is amazing.
"Thank you all so much we are so grateful.
"I only set 10k as a rough target as we have no clue how much it will all cost and this is just amazing.
"I want to thank you all from the bottom of my heart.
"So lets continue to push and share and donate to help out this wonderful lads family.
A spokesman for the Foreign and Commonwealth Office said: "We are supporting the family of a British man who died following an incident in Sofia, and our staff are in contact with the UK and Bulgarian authorities."
The Bulgarian Ministry of Interior said after his death on Monday: "A 32-year-old man has sadly died.
"At 10am, the police received a signal to attend a man in a helpless condition, in the city centre.
"He was a foreign national, from Britain, and he was taken to hospital but he sadly died.
"Police are working to clarify all the circumstances in the incident. There is no further detail on any injuries.
"There will be a forensic examination to find out what the cause of death was."
A statement on the authority's website claimed that the victim "suddenly began to act aggressively" in hospital but offered no further detail on the circumstances.
England won the qualifier 6-0 in a match that was marred by racist chants and gestures from sections of the Bulgarian crowd.