The 51-year-old was not present at the FA Cup final on Saturday that saw Chelsea emerge victorious over Manchester United at Wembley stadium. The win earnt The Blues their first piece of silverware this season.
Abramovich's office said they do not discuss personal matters with the press. Yet, according to the 'BBC's' source, there is an issue with his visa renewal.
It is thought that the Russian's investor visa had expired last month, although the British Home Office also refused to comment on the situation.
The delay coincides with a cooling in diplomatic relations between the UK and Russia, following the suspected politically-motivated poisoning of former Russian spy Sergi Skripal in England, an accusation that Moscow denies.