Saints meet United in the early kickoff today.
Shearer told Betfair: "Southampton have to start picking up points, especially now Leicester don’t look to be getting deducted any points.
"Southampton have been struggling to put the ball in the back of the net and finishing the chances they’ve created.
"When they do get them, they have to start taking them. That's where they have to improve massively."
He continued: "I think Man United have been bang average so far this season, which is why there's a lot of talk around ten Hag.
"This is a huge game for both clubs and could have huge ramifications going forward. There'll be so much noise if Man United don't win this game.
"Particularly with the start to the season Southampton have had too. If Man United were to go there and fail to win, or even worse, be beaten...
"The noise around the job and everything else at the club would rank up a notch or three. I'll go for a draw."