Watson was twice out lbw cheaply in all-too familiar fashion as England, against many pre-series predictions, won the first Test in Cardiff by the crushing margin of 169 runs with more than a day to spare last week.
With his medium-paced bowling barely used by captain Michael Clarke at Sophia Gardens, Australia's Fairfax Media reported Wednesday that the 34-year-old Watson would be dropped at Lord's and replaced by fellow all-rounder Mitchell Marsh, 11 years his junior.
"My gut feeling is they'll probably go with Mitchell Marsh," former Australia captain Steve Waugh told Sky Sports before the Fairfax report, subsequently cited by Cricket Australia's own website, was published.
"A guy at that age... When he's played a long time, when you make a decision like this now -- it's pretty much final. There's probably no way back from being dropped now."
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Marsh, the son of former Australia opener Geoff Marsh, has played in four Tests and impressed in the team's opening two tour matches by scoring hundreds against both Kent and Essex.
Haddin, 37, withdrew on Tuesday for what a team spokeswoman said were "family reasons", although he will remain with the squad in London.
Peter Nevill, also Haddin's New South Wales deputy, is now set for an international debut on Thursday.
This is not the first time Haddin has put his family ahead of his cricket career. In 2012, Haddin took several months out of the game after his then 17-month-old daughter Mia was diagnosed with neuroblastoma -- a rare form of cancer.