Eriksson has been out of work since leaving Championship side Leicester last October.
Chelsea axed Andre Villas-Boas on Sunday, just eight months since taking charge at Stamford Bridge.
When asked if he would be interested in the Chelsea job, Eriksson told Sky Sports News: “I would take it, of course.
“They already have a manager for the rest of the season (Di Matteo) and I guess that is a natural solution, because he has been in the club now for the whole season.”
Chelsea’s next manager will be their eight manager in nine years.
Eriksson added: “Nothing is impossible. But this time I think it is understandable that something (Villas-Boas’ sacking) happened.
“I don’t defend it. But I can understand it, because with Chelsea if they don’t play in Europe next season, that would be a disaster for them.”
