Mourinho is understood to be considering the veteran forward as back up in case the clubs move to bring Manchester United’s Wayne Rooney to Stamford Bridge falls flat.
Chelsea remain confident of signing the 27-year-old England striker, and are thought to be preparing a third bid believed to be in the region of £28million.
However Mourinho has begun looking at back up options, as United manager David Moyes once again stated Rooney would not be sold this summer after his side’s 2-0 win over Wigan in the Community Shield.
It is understood Mourinho has made an enquiry to Russian club Anzhi Makhachkala over a possible £5million deal for Eto’o.
The Russian club are willing to sell, having recently been hit by a financial crisis.
Mourinho is a big admirer of the Cameroon striker, having previously tried to bring him to Stamford Bridge during his first spell as Chelsea boss.
Eto’o was part of Jose Mourinho’s treble winning side at Inter Milan, and the pair have kept in touch since.
Mourinho still believes the 32-year-old could do a job in the Premier League, and would represent a far cheaper alternative to Rooney.
Eto’o moved to wealthy Russian outfit Anzhi from Inter in 2011, although now the club have been forced to put every player up for sale to slash their budget in half.
[cat_link cat=”chelsea” type=”grid”]