The Russian club have decided to slash their budget in half due to a change in policy and owner Suleyman Kerimov's poor health, but according to Eurosport, they will not be flogging their big-money purchases on the cheap.
Eto'o has entered the final year of his mega contract and is widely expected to see it out—after all, Anzhi is the only club that will be willing to offer him close to £250,000 per week.
However, his availability has caused a number of clubs to give him more than a passing glance, and the Cameroon international could well fancy a final flirt with UEFA Champions League football.
LA Galaxy's reported interest, via The Times (h/t Fox Soccer), is likely to be blown out of the water for the time being, while former club Internazionale would also struggle to bring him in given they're in the process of rebuilding.
That leaves Chelsea, who as we know are in for a forward this summer.
The two worked together at Inter in 2010, famously delivering a historic Italian treble after defeating Bayern Munich in the Champions League final, and there have been suggestions Mou checked on him during his first stint with the Blues.
At 32 years of age, Eto'o is no long-term fix. However, if Mou is concerned Romelu Lukaku cannot handle an entire season as the focal point of an attack expected to win the league, the Cameroonian is an ideal stopgap.
Eto'o has more than enough experience and nous to help guide and lead, having played for Barcelona and Inter, and represents a far more versatile and well-rounded option than many give him credit for.
He played largely as a wide man at Inter under Mourinho to accommodate Diego Milito, while at Barca he drifted from the right fairly often, too.
At Anzhi, he's played a variety of positions, turning out to be surprisingly efficient in the No. 10 role behind target striker Lacina Traore.
He's not simply a finisher, and combines pace and power with decent control and awareness, good dribbling and now, as a result of his time in Russia, great linkup play, too.
Perhaps not quite the complete modern forward Mourinho would ideally like to hang his hat on, but given what's available, a punt on Eto'o on a short-term contract would be a very wise move indeed.
Fox Soccer have suggested Anzhi want £13 million for Eto'o, which is preposterous. However, if his signature can be secured from £8 million or less, it's good business.
If Plan A (Rooney) falls through, you cannot really go wrong with Eto'o as a Plan B.