England prop Joe Marler is being investigated by the Rugby Football Union after an obscene remark directed at former Australia coach Bob Dwyer was posted on his Twitter account.
Dwyer claimed England tight-head Dan Cole scrummaged illegally during the win over the Wallabies on Saturday.
The RFU has strict guidelines on the use of social media.
Marler is not on tour, having asked to miss the trip in order to “recharge his batteries” after a difficult season.
In April he was fined £20,000 and given a two-week ban for calling Wales prop Samson Lee “Gypsy boy” during the Six Nations.
The Harlequins prop was suspended for a further two weeks for kicking Grenoble hooker Arnaud Heguy in his first game back.
Loose-head Marler was accused by Dwyer of scrummaging illegally during the build-up to England’s World Cup group game against Australia last year.
The offensive tweet – which said “Bob Dwyer is a wanker” – was quickly deleted from Marler’s account.
Eddie Jones’ side will seal England’s first series win in Australia if they win the second Test in Melbourne on Saturday.