The Red Devils are currently second in the Premier League table, three points behind leaders and rivals Manchester City.
However, Shearer believes that the management skills of Sir Alex Ferguson could see United come out on top.
"It wouldn't surprise me if Manchester United win it," the former Newcastle United striker told BBC Sport.
"With the old wily fox Sir Alex Ferguson in charge, I wouldn't be surprised if they pipped Manchester City and Tottenham."
Shearer turned down the chance to join Man United in 1996.