Sergei Skripal and his daughter, Yulia, are in a critical condition after the incident in Salisbury on 4 March.
Prime Minister Theresa May said on Wednesday that the relationship between the two countries “cannot be the same”.
It was previously reported that Prince William, the president of the Football Association (FA), would not attend.
When asked whether senior FA officials should also not go to the World Cup – which runs from 14 June to 15 July – Mrs May said: “I’m sure they will want to be considering their position.
“Attendance at sporting events is a matter for the sporting authorities – it’s a matter for them.”
On Tuesday, the FA had made no changes to plans for England’s presence in Russia.
Mrs May, speaking at Prime Minister’s Questions, said the government would “look at security and protection of any UK football fans travelling to the World Cup”.
She also announced that the UK will expel 23 Russian diplomats and revoke an invitation to the Russian foreign minister to visit the country.
Russia denies being involved in the attempted murder of Sergei Skripal.