Shields was jailed for 15 years in Bulgaria for the attempted murder of a barman following Liverpool's 2005 European Cup win. The conviction was a farce and another man, Graham Sankey, signed a confession, later withdrawn.
Straw has said his decision is provisional and Shields's lawyers have a month to put forward more evidence.
"I understand, of course, the strong emotions felt by the Shields family and his many supporters in Liverpool and way beyond Liverpool," said Mr Straw. "What I ask people in return is that you have to operate in this country by the rule of law," he said.
"Of course, I am open to further representations from Mr Shields and I am seeking them."
"We are absolutely devastated by today's announcement from Jack Straw," said Shields's father Michael senior.
"After four years of tireless campaigning, we had every hope and belief that Michael was about to be pardoned for a crime he did not commit. I have spoken to Michael and he is absolutely distraught.
"We have been led a merry dance by the Government.
"We have been kept completely in the dark and still have no idea what is happening.
"Michael received an email in prison today telling him his pardon had been refused, but he does not know the reason why.
"I don't know how much more we can take as a family."