It comes just days after similar legislation was scuppered at Westminster.
Labour Wants To Call Time On Booze Ban
Scottish Labour has revealed plans for a consultation on alcohol sales at football grounds.
A meeting will be held at Hampden on Friday to allow the party to gauge views.
Representatives from the Scottish Football Association, football clubs and Police Scotland will be invited to attend.
Labour will also consult the public via its website, football forums, Twitter and Facebook, and members will hand out leaflets at matches asking for supporters' opinions.
Mr Murphy said: ``In a country where rugby fans can rightly drink and corporate hospitality football fans can rightly drink, today's generation of football supporters are paying for the sins and the crimes of Scottish football fans from 1980.
''I think we should stop criminalising football fans and stop treating them as uniquely incapable of drinking in moderation and enjoying a sporting occasion.''
The MP said the attitude towards football fans in Scotland had a degree of `` a kind of class prejudice''.
Celtic fan Mr Murphy, who is teetotal, said: ''As someone who loves football and who wants to keep football what it has become - a family sport - I think we should try the careful introduction of drinking alcohol in football stadia and listen to football's opinion.
''It's about treating football fans as adults and, done properly, it can improve the experience of the stands. This can't and shouldn't be driven by a desire of football clubs to boost their income or fleece supporters.
''We are going to do a really comprehensive consultation, initially with football supporters and finally with people who live near football grounds, for example.''
The alcohol ban was initially imposed following a riot at the 1980 Scottish Cup final between Rangers and Celtic but alcohol can be served in corporate hospitality areas of football stadiums.
A Scottish Government spokeswoman said: ''The vast majority of football fans in Scotland are well behaved, and a credit to their clubs, but the current policy on alcohol at football grounds was introduced for good reasons and the view of the police is that it should remain in place.
''Groups offering support to victims of domestic violence also strongly support the policy remaining as it is, given the marked increase in domestic abuse incidents which has been recorded in relation to some football matches.
''Having stadiums as alcohol-free zones has helped Scottish football to become the family-friendly experience it is for so many people today, and it is important not to jeopardise or undermine that success story.''
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