The Russian billionaire was not present at Wembley Stadium on Saturday evening to watch the Blues lift the FA Cup following their 1-0 win over Manchester United.
According to the Financial Times, the 51-year-old's request has not been rejected by the Home Office, but the process is taking an unusually long time.
Abramovich, worth an estimated £8.3bn, is understood to have last visited London in early April, a few weeks before the visa expired.
A source is quoted by the publication as saying: "There's something up with his visa. I don't know what it is and they don't know what it is either. Let's hope they sort it out soon."
Both the Home Office and Abramovich's spokesman have yet to comment on the article.