Eto’o, 33, is a free agent after his contract with Chelsea expired this summer and he spent the weekend in talks with Ajax over a possible move to the Amsterdam Arena.
But his preferred destination is Inter, the club with whom he won the treble during a brilliant two-year spell between 2009 and 2011.
The club’s president, Erick Thohir, is currently against the idea of re-signing the forward due to his age and salary – which would be at least €4-5 million (£3.2-4m) a season.
Coach Walter Mazzarri is in the market for a frontman to complement current attackers Mauro Icardi, Dani Osvaldo and Rodrigo Palacio but would prefer a second striker rather than another dedicated penalty-box player.
But the ex-Barcelona star is not giving up just yet and, despite having offers on the table from both Ajax and Wolfsburg, he is prepared to give Thohir and Mazzarri more time to change their minds. The veteran will wait at least another week in the hope of receiving good news.
In July, Eto’o had agreed a potential transfer to Juventus but, after discussions with the player’s representatives, the Bianconeri decided that his wages were too high.
The veteran originally joined Inter as part of a swap deal involving Zlatan Ibrahimovic five years ago, with Barcelona paying €46 million (£36.7m) for the Sweden star as well as allowing Eto’o to move in the other direction.
Under Jose Mourinho he scored 33 goals in 67 Serie A appearances before leaving the club for Anzhi Makhachkala in 2011.
He teamed up with Mourinho at Chelsea for the 2013/2014 season but the two fell apart after the Portuguese manager was caught on tape questioning the player’s age.
Eto’o left the Stamford Bridge club calling Mourinho a “fool” and “puppet”.