Foreign Affairs Select Committee chairman Tom Tugendhat and Chris Bryant, chairman of the All-Party Parliamentary Russia Group, have urged a boycott of the tournament if it is proved that the assassination attempt on former Russian spy Sergei Skripal in Salisbury is linked to the Kremlin.
The Duke of Cambridge, the FA president, is said to have no plans to attend and it is likely that no government ministers will go if a link is proved.
However, Dyke has claimed that the FA - who would risk being banned by FIFA from future tournaments if they did pull out of Russia - is unlikely to withdraw the team from the tournament.
"I can't see the Russians being too worried if a bunch of bigwigs from England decide not to go," the 70-year-old told the Daily Mail. "The FA pulling the team out would be another matter but I can't see that happening."
British sport and politics were at loggerheads in 1980 when the British Olympic Association ignored a request from Margaret Thatcher to boycott the Moscow Olympics following the Soviet invasion of Afghanistan.