The Mexican international was a £4million signing for Celtic two years ago, but has been in limbo since returning to the Parkhead side following his loan spell in Spain.
Manager Neil Lennon said: "Efrain hasn't figured that much this season, even during his loan time at Zaragoza, and it might be best for him to move on and try to further his career elsewhere."
Those who are set for pastures new, such as Mark Wilson, Daniel Majstorovic and Glenn Loovens, will get an opportunity to say their goodbyes to the Hoops support on Sunday – although they won't necessarily find themselves getting game time.
"The whole team will be there to celebrate picking up the trophy on Sunday against Hearts, but whether or not they'll be in the squad is another matter," said Lennon.
Meanwhile, Lennon has insisted that Kris Commons will be going nowhere. The midfielder scored his first goal of the season in the final Old Firm game of the campaign less than a fortnight ago and he has been a sporadic performer for the club this term.
Lennon, though, has insisted that recent form has underlined Commons' ability and, if he stays injury-free, will be a key figure next term.
"Kris will not be going anywhere," said Lennon. "He has a major part to play in this squad next season and the same goes for Emilio Izaguirre.
"It might look as though the season is ending at the wrong time for them, but they can hold on to what they have produced over the last month.
"The only thing that happened to these guys was the fact they were so unlucky with injury.
"I have never doubted their ability or the fact that they would get back to playing at this kind of level, regardless of how others may have seen it."