The Manchester United forward only managed 20 minutes in the team's last two friendlies against Brazil and Belgium.
The likes of Anthony Gordon were given more game time, with Rashford now sweating on his place for the tournament.
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Shearer told The Athletic: "If Rashford plays well between now and the end of the season then that could potentially force the manager's hand. But I don't think he's a certainty to go, no.
He's not a center-forward, he doesn't want to play there. He'd be going as a wide forward who can play as a striker in an emergency.
You can tell from his body language that he doesn't want to play there for Manchester United. If he's going to be in the squad, it wouldn't be ahead of Harry Kane, (Ollie) Watkins or (Ivan) Toney, it'd be as a wide forward."