The Swede was linked with a move to Manchester United a year ago but has always said he is happy with his job as England coach and it would be a severe blow to the international team's chances of qualifying for Euro 2004 if he was to leave now.
The future of present Chelsea manager Claudio Ranieri has been the subject of some speculation since Abramovich took over but the Italian seemed to be safe for the time being.
A host of top European players have already been linked with Chelsea and Abramovich would see the arrival of Eriksson as an enormous advantage in persuading star names to sign for the club.