Paddy Power have offered a special market on what Redknapp's next job will be, with a return to West Ham, where he was the manager for seven years between 1994 and 2001, chalked up at 4/1 (5.0).
However, that possibility only seems likely should West Ham United, under the stewardship of Sam Allardyce, endure a poor start on their return to the English Premier League next season.
A return to Southampton, priced up at 15/2 (8.50) with Paddy Power, who are currently managed by Nigel Adkins, would appear equally unlikely for the same reasons.
Paddy Power also go 15/2 (8.50) on Redknapp next being employed by Queens Park Rangers, but Mark Hughes seems to have secured, at least, his short-term future by steering the club to safety on the final day of last season.
Everton, priced up at 10/1 (11.0) may have been a possible destination for Redknapp had David Moyes replaced him at White Hart Lane but, with that seeming unlikely, there appears to be no vacancy at Goodison Park either.
Redknapp, of course, was a hot favourite for the England job a few short months ago and Paddy Power offer 11/2 (6.50) that he will replace Roy Hodgson in the Three Lions hot seat as his next job.
Hodgson, though, has performed admirably in the role so far and, surely, will retain his role beyond the summer, thus meaning that Redknapp may need to look further afield to find immediate employment.
The former Portsmouth manager has suggested that he is not averse to relocating from his Dorset home to find a fresh challenge and Paddy Power offer 20/1 (21.0) that he will take up the reins at LA Galaxy, replacing Bruce Arena as manager.
Arena's Galaxy, though, enjoyed a successful season last term and it seems unlikely that they should wish to part with their head coach at this time.
Harry Redknapp's next move, then, seems less than certain but, with his insistence that a fresh challenge may be just around the corner, all eyes will most certainly be on the managerial merry-go-round.
Harry Redknapp's next job? (Paddy Power)
West Ham United at 4/1 (5.0)
England at 11/2 (6.50)
Southampton at 15/2 (8.50)
Queens Park Rangers at 15/2 (8.50)
Everton at 10/1 (11.0)
Newcastle at 10/1 (11.0)
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Willie Duncan is a freelance sports journalist. Willie, from Edinburgh, has covered Scottish football for over 10 years and he specialises in football betting markets from across Europe. You can also follow Willie on Twitter here.