The Argentina international has declared he wants to eventually return home and play for River Plate.
"Today it is honestly very difficult, I owe myself to Monterrey," Funes Mori told La Nacion.
"Later on we will have to see how I am physically, I don't want to go back and not be able to move, but I dream of going back one day."
Funes Mori admits his previous spell with River was a difficult period for the club.
"I had to play in a very difficult moment in the history of River and I would have loved to stay to live what my brother (Ramiro) lived through; eliminate Boca twice and win the Sudamericana (2014) and the Libertadores (2015)," he added.
The 29 year-old striker is Monterrey's second-placed all-time leading goalscorer.