News of the World says the former Barcelona boss is interested in the job.
Chelsea stand-in chief Guus Hiddink discussed the job with Rijkaard last week.
Hiddink plan to return to his job as Russian national team manager in the summer.
A source told News of the World: “Guus and Frank have had long discussions about the job in the last few weeks. It has been informally agreed Frank will step in during the summer.
“Abramovich wants Hiddink to complete Russia’s World Cup campaign — but there will then be the option for him to return to Chelsea and work in tandem with Rijkaard.”
