Burke, who has been in good form with English Premiership side Newcastle Falcons, was sent an SOS by Wallabies coach John Connolly in March after Chris Latham suffered a season-ending knee injury.
The 34-year-old rejected the chance to join the Australian team for the upcoming Test season beginning in May. But a knee injury to Latham's probable successor, Cameron Shepherd, has renewed calls for Burke to return.
However, Jones - Burke's mentor over the last four years with the Wallabies, poured cold water on the suggestion.
"Burkey is 34 and in those positions you don't get better with age because speed's such an important thing," Jones told the West Australian.
"Certainly he's got the experience and he's playing well in England, but you've got to remember England is a club Premiership, it's not Test level. It's much slower than Test level."
Jones claims the Reds' rugby league-convert Clinton Schifcofske is a much better option.
He has impressed in his first season in the Super 14 and is a noted big-game player, having starred in Australian rugby league's biggest annual tournament - the State of Origin series between Queensland and New South Wales.
"With Latham out, then you think about looking at someone like a Clinton Schifcofske, who will do a job for you and kick goals, which is important," Jones added.
"The other idea might be to put someone like Lote Tuqiri at full-back."
Other possibilities for the role include former winger Drew Mitchell, who has been installed ahead of Shepherd at number 15 for the Western Force, or Brumbies versatile utility back Julian Huxley.
Shepherd is aiming to make his comeback against Wales in Sydney on May 26.
The 23-year-old, who has been a revelation in the Super 14 competition this season, was thought to have suffered a season-ending knee injury during his side's 14-12 loss to the Brumbies on Friday night.
However, scans on his left knee revealed only a minor tear and he is now setting his sights on returning against the Welsh.
"People are saying four to six weeks but fingers crossed I'll be back sooner," Shepherd told The Daily Telegraph.
"My goal is definitely to try and get back for the first Test match if I am selected and that is five weeks away."