The 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 fly-half was arrested on suspicion of drink-driving on Monday and later released on bail.
Cipriani, 27, has not been charged and will meet up with the rest of England's World Cup training squad on 22 June.
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 on Monday morning, 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 on Sunday.
Cipriani, who has played in 12 Tests, was named in Stuart Lancaster's 50-man England training squad for this year's World Cup.
|Danny Cipriani's Test career|
|12 matches||Four starts||Eight as replacement|
|Two tries||Eight conversions||11 penalties|
England's build up to the home tournament, which starts in September, has been hit by off-field issues.
Last month, Lancaster dropped Manu Tuilagi after the Leicester centre admitted assaulting police officers.
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.