Following Friday's disappointing defeat to Montenegro, current boss John Toshack is said to have reached the conclusion that it would be better if he moved on.
And Giggs' name has been mentioned as the Football Association of Wales' first choice.
Going strong: Ryan Giggs' playing career shows no signs of ending
Mark Hughes did something similar when his own playing career was coming to an end at Blackburn, with Harrison acting as a key member of his back-up team.
However, the man responsible for bringing Giggs through the Old Trafford ranks as part of that famed 'Class of 92' does not believe it would be possible for the 36-year-old wide-man to combine duties at a club like United.
'It is not a cushy little number and it is not a part-time post,' he said.
'You are at the sharp end of things and these days I don't believe you could combine playing for a club at United's level and managing an international team.
'When I was with Mark we'd be jetting off all over the place watching future opponents. Then you would be going up and down the country checking on your players.
Father figure: Harrison (centre) with players from the famed 'Class of 92'
'You couldn't be playing for United at the weekend and be wondering and worrying about how the Welsh players are doing.
'If the vacancy does come up and Ryan is approached then he has a massive decision to make.'
Harrison has no doubts Giggs is mentally tough enough to make a success of the management game and will become Wales boss eventually.
However, having amassed a record 11 league titles as part of a medal collection unmatched in the modern game, it is hard to imagine Giggs merely turning his back on it at a time when his overall influence is as high at it has ever been.
Giggs extended his record of scoring in every Premier League season with a volley against Newcastle last month and he was an influential figure in the subsequent victory over West Ham.
Sir Alex Ferguson recently suggested the Cardiff-born player, who was only ever eligible to play for Wales despite his appearance for England schoolboys, could continue until his was 40 such are his fitness levels.
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