The Mexican international was signed again by former Rangers manager Pedro Caixinha in January on loan from the Ibrox club until the end of the year.
However, his return to the Mexico City club has been a disaster. He has barely played after an ankle injury and was booed by his own fans when he did feature because of lacklustre performances.
This week, he reached a new low when he was caught buying a six-pack of beer while wearing his Cruz Azul gear after a training session next to the club’s La Noria complex in Mexico City.
That caused Cruz Azul boss Caixinha to warn him he would consider ripping up his loan contract and order him to return to Glasgow.
And former team-mate Mauro Boselli even went so far as to advise Pena to seek help for his “issues” after the incident.
Now Cruz Azul president, Guillermo Alvarez, has announced the player’s future will be discussed this week.
He said: “Carlos Pena’s future at this club will be decided in the coming days. We will look at all options concerning the player, including his contract situation.”
Rangers reportedly paid £2 million for Pena, pictured, last summer and are still paying a sizeable chunk of his £26,000-a-week wages.
The midfielder still has two years of his contract left at Ibrox, with Cruz Azul now looking extremely unlikely to take up their purchase option on the 28-year-old.
Pena scored five goals for Rangers in eight starts and six substitute appearances during the first half of the season before returning to his native Mexico at the start of the year.