A report from Calciomercato in Italy indicates Rodriguez is unhappy with his circumstances in Qatar with current club Al-Rayyan, and wants to leave.
The Italian site claims Galatasaray had been the favourites to pursue a move for the 30-year-old, but fresh interest from Colombian side Junior Barranquilla, or Junior FC, had surfaced.
Junior FC would reportedly be willing to take on the 2014 Colombia World Cup hero, with a transfer fee of 15 million Euros being requested by Al-Rayyan.
Rodriguez joined the club in September 2021 after being frozen out of the squad by then Everton manager Rafael Benitez, an appointment which has left Everton with their Premier League status in jeopardy.
The attacking midfielder joined Everton in 2020 from Real Madrid to play under Carlo Ancelotti, and scored six goals and registered nine assists in 26 games for The Toffees that season before Ancelotti returned to manage Real Madrid.
Rodriguez has scored five goals and laid on seven more in 15 games for his current club. He has a contract with the outfit until 2024, but a return to his homeland could be what he desires after a turbulent few months for him.