At the weekend, Mourinho hinted Chelsea will bid for Monaco striker Radamel Falcao in the summer after their initial target, Wayne Rooney, committed the remainder of his elite career to Manchester United.
Eto'o, Fernando Torres and Demba Ba have scored just 18 goals between them this season and Mourinho has not been hesitant in expressing his doubts about the trio.
Shortly after arriving in Istanbul ahead of the Blues's Champions League round-of-16 first leg with Galatasaray, Mourinho was recorded by the French television company Canal Plus in what he thought was a private conversation with the owner of Swiss watch manufacturer Hublot.
"I have a team but no striker," said Mourinho. "The problem at Chelsea is that we are lacking a goalscorer. I have Eto'o but he is 32, possibly 35, who knows?"
The joke about Eto'o's age is a reference to unfounded allegations that African footballers claim they are younger than they are.
Earlier this month, Lazio threatened legal action following questions over youth teamer Joseph Minala's age. Supposedly 17, an African website listed his age as 41.
Torres has cored just 43 goals since his £50 million transfer from Liverpool three years ago, Ba has scored three in 18 this term and Eto'o, labelled "Plan B" by Mourinho in the summer, has hit winners against Liverpool and Manchester United.
At the weekend, Mourinho told Canal Football Club: "I have a team, but no striker. Falcao does not have a team. A player like him can't play in front of 3,000 people. Monaco is a club to end your career with."
Mourinho, however, ruled out a reunion with his former Internazionale frontman Zlatan ibrahimović, or a move for the Swede's Paris Saint-Germain teammate Edinson Cavani.
Chelsea are keen on Atlético Madrid's Diego Costa, thriving at the Vicente Calderón in Falcao's absence.