The Frenchman is currently halfway through a two-year loan spell, but the deal includes a compulsory transfer clause, which would see Atletico pay Griezmann's parent club Barcelona €40 million (£34.03m).
Although the 31-year-old only returned to the Metropolitano Stadium last summer, he could head through the exit door in the current transfer window.
According to The Times, the La Liga side are looking to offload Griezmann in a bid to free up space on their wage bill to make a move for Ronaldo.
A recent report suggested that Atletico are weighing up a move for Ronaldo, who is keen to sign for a Champions League club.
Despite playing for Atletico's city rivals Real Madrid, Ronaldo is open to the move after Diego Simeone demonstrated an eagerness to work with the Portuguese international.
After returning for a second spell with Atletico last summer, Griezmann scored eight goals and contributed seven assists for Simeone's side in the 2021-22 season.