Chelsea owner Roman Abramovich is eager to install a new manager quickly after yesterday's dismissal of Avram Grant.
Chelsea need to find a replacement quickly to input into the summer transfer planning, with Rijkaard available after leaving Barcelona and Mancini expected to be replaced at Inter Milan by Jose Mourinho.
Mancini has a more impressive recent record, having won the past three Serie A titles in Italy, but he has failed in the Champions League.
Rijkaard, currently on holiday in the United States, won the Champions League in 2006 and Spain's La Liga in 2005 and 2006, but he has failed to capture a trophy in the past two seasons and was sacked by Barcelona earlier this month.
Hiddink has yet to finalise his contract with the Russian national team, which is bankrolled by Abramovich.
The Dutchman has verbally agreed to stay with Russia until 2010 but the deal has not been ratified and so he remains a potential candidate.