Van Gaal last month lamented the fact that his current squad does not have a striker pushing to reach the milestone in the Premier League this season.
Wayne Rooney is United's top scorer in the league with 11 goals this term, despite playing large parts of the season in midfield, while Robin van Persie has 10 in an injury-hit campaign.
On-loan Monaco man Radamel Falcao has struggled for form since moving to Old Trafford and it remains to be seen if the Colombia international will still be at the club next season.
Sheringham, who was part of the famous treble winning team of 1999, feels that the easiest solution would be to play teenage striker Wilson - who has one goal in 12 league games this term - alongside captain Rooney.
Speaking to United Review, he said: "I really like James Wilson. It's a shame for him that Radamel Falcao and Robin van Persie are in front of him.
"Louis van Gaal said recently that he doesn't have a striker who can score 20 goals a season, but I think if you put Wilson up there with Wayne Rooney then you'd have two players who can reach those figures for you.
"He's very direct, scores goals, has good pace and that added bonus of being a left-footer - they always tend to catch defenders off guard and it always looks more special when the left-footed strike goes in.
"I like his attitude, he looks a good player, a good prospect and one that everyone needs to keep an eye on."
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