The Chile international has been heavily linked with a move to Manchester United, despite initially being touted as a top target for Manchester City.
At the moment, the deal seems to be hanging in limbo, which has caused some to question the timing of Mayte Rodriguez's social media post.
The Chilean actress, who is in a relationship with the footballer, wrote: "The greatest storms of our lives demonstrate the strength of our anchors."
A post shared by Mayte Rodriguez (@mmayte_rodriguez) on
According to the Manchester Evening News, Sanchez, who has not posted anything on social media since January 2, 'liked' his girlfriend's update.
If the 29-year-old does not leave Arsenal in this window, he will be eligible to join another club for free when his contract expires in the summer.