Rangers transfer latest: Midfielder to leave for Turkey? | Davis agrees £12k-a-week deal | Winger set for early return
Since signing from Chivas in 2017 when Pedro Caixinha was manager, Pena has played just 14 games and has spent time with Cruz Azul and Necaxa.
The 28-year-old has 18-months left on his deal and is one of the club's higher earners. Steven Gerrard is keen to get the player off the wage bill, whether it is a loan or permanent deal.
Pena's place in the squad will be taken by Northern Ireland international Steven Davis.
The 34-year-old has been keen on re-joining Rangers having spent four-and-a-half seasons with the Ibrox side earlier in his career, playing more than 200 times and winning a glut of trophies.
The Scottish Sun report that the player has agreed a deal in principle to return.
Davis has been given permission to leave Southampton for free this month and will take a substantial wage cut to sign for 18 months on a £12,000-a-week deal.
The club hope to have the move completed before heading off on their winter break in Tenerife.
Rangers have also been boosted by the news that Jamie Murphy will make a return before the end of the season.
The winger has been out of action since sustaining an ACL injury at Kilmarnock in August.
He told RangersTV that his aim is "to get outside".
"I never thought I would be looking forward to running so much," he said. "I can’t wait to get outside, put the boots on and even just go a jog.
"I have got a date in my head. The surgeons told me a date and he pretty much said the season, but we will see how it goes.
"I always find myself to be a quick healer so we will see how the next couple of months go."