England's Rugby Football Union says it will wait until a police investigation into Danny Cipriani is concluded before deciding if any action is needed.
The England and Sale first-five was arrested on suspicion of drink-driving and later released on bail.
Cipriani has not been charged and will meet up with the rest of England's World Cup training squad later this month.
An RFU spokesperson said it would be "inappropriate to comment at this time until all the facts are known".
Cipriani was involved in a car crash, hours after England's 73-12 win against the Barbarians.
He was given a breath test and taken to a west London police station before being released.
The Sale star scored two tries and was named man of the match during England's victory at Twickenham.
Cipriani, who has played in 12 Tests, was named in Stuart Lancaster's 50-man England training squad for this year's World Cup.
Cipriani is the latest England player to be involved in off-field problems.
Leicester centre Manu Tuilagi was convicted of assaulting two female police officers and a taxi driver and will not feature in the World Cup being played in England.
Northampton hooker Dylan Hartley has also been excluded from the competition by the England head coach after being given a four-week ban for head-butting Saracens' Jamie George during a Premiership game.
Cipriani made his England debut in 2008 but fell out of contention for four years after injury, off-field problems and a move to Australia.
He returned to the international fray after impressing at club level with Sale and played in three matches during the 2015 Six Nations.