Speed, 42, was found hanged at his home in Cheshire early on Sunday morning in an apparent suicide and an inquest into his death will be opened later on Tuesday.
"I'd love to see Wales play a game in an international week against players from his former clubs," the 53-year-old Southall, a former Wales and Everton team mate of Speed's, told British newspapers.
"Get some of the Newcastle lads down, Everton, Bolton, Sheffield United, Leeds and dedicate the game to his family.
"You don't know what sort of state his finances are in. Pack the Millennium and everyone can pay their respects. If that can't be done, I'd like to see a proper footballing power turn up. It would be sombre, but a success."
Southall also said the Wales Footballer of the Year Award should be named after Speed who had begun to transform Welsh fortunes having led them to three wins in a row.
"It'd be nice if they name the Wales Player Of The Year award after Gary. Name a stand after him. It would be nice for Everton to do something."
Everton have said that his team mates from 1996 to 1998 will be invited to Goodison Park on Sunday for the match against Stoke City as part of a tribute to their former midfielder, who was also a boyhood Everton fan.
BOOK OF CONDOLENCE
There will also be a minute's silence before the Premier League fixture and the club have opened a book of condolence.
Leeds fans will sing Speed's name for 11 minutes from the 11th minute of Tuesday's Championship match at Nottingham Forest. Speed wore the No. 11 shirt during his eight years at the club.
There has been an outpouring of stunned public grief following his death with so many tributes pouring into the Football Association of Wales's online book of condolence that it crashed on Monday.
PFA Chief Executive Gordon Taylor said: "There will be an overwhelming sense that we want to do something together to show how loved and regarded he was in the football world. There is a terrible sense of loss."
Speed's close friend, former England striker and Newcastle team mate Alan Shearer, summed up what many felt when he wrote in The Sun: "The question I keep asking myself, and have done so since I heard the dreadful news, is: Why?
"I was with him on Saturday for most of the day. There was not an inkling of anything wrong with him. He was his usual bright, cheerful, mickey-taking self."
Shearer said the two had made plans to go on holiday with their families to Portugal again as they did this year, and that Speed planned to stay at Shearer's house next Friday after a charity event in Newcastle.
"When we parted on Saturday he made some jokey remark about my golf. 'See you next weekend' were his last words to me.
"They were not the words of someone planning to do something so awful."
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