Koeman arrived at Barcelona earlier in the month following Quique Setien's sacking, and was immediately tasked with restoring calm at the club following months of unrest.
The 57-year-old's position has been made more difficult by the situation surrounding Messi's future, with the six-time Ballon d'Or winner having handed in a transfer request and refused to return to training.
Amid the ongoing fallout, the ex-Netherlands boss has been encouraged to sell his star player by former Egypt international Mido, who worked under the Dutchman at Ajax Amsterdam.
"The best thing that could happen to Koeman is the potential departure of Messi. Koeman won't be able to build his empire with Messi existing in the dressing room.
"Koeman was my coach for two-and-a-half years and no matter how much time goes by, he is still unable to handle players with strong characters and he doesn't want a player who has an opinion."
Messi failed to show up to Barca's mandatory COVID-19 testing on Sunday and was absent again without permission for the team's training session on Monday morning.
