The former skipper at Craven Cottage is leading the bookies market as they sit bottom of the Premier League.
David Moyes was the former favourite but he is now second in the market at 7/2, behind Parker who is just 3/1.
Parker is currently a first-team coach under Jokanovic at Fulham and could make the step up.
Meanwhile Sam Allardyce, who has never been relegated in the top flight, is 6/1 to take the job ahead of another former favourite Chris Coleman.
Jokanovic is now odds-on in the Premier League sack race after a shocking start to the season.
The Serbian's odds of being sacked were slashed after the Cottagers slumped to a sixth consecutive defeat against Huddersfield on Monday evening.
Betway’s Alan Alger said: “Monday’s loss to Huddersfield piled the pressure on Jokanovic and with his side rock-bottom of the Premier League, we’ve opened betting on his replacement.
“Former Cottager Parker, who is one of Jokanovic’s backroom staff, heads the betting at 3/1, with David Moyes hot on his heels at 7/2.
“Sam Allardyce prides himself on getting clubs out of tricky situations and he could be a viable option at 6/1, while club favourite Chris Coleman also looks in the running at 7/1.”
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