The Tannadice match is a replay of last month's game that was abandoned due to flooding and many Rangers fans are not willing to buy the half-price tickets, reports BBC Sport.
The home fans have bought 7,000 tickets but boss Levein wants United supporters to increase their numerical advantage.
He said: "It will mean a lot to have most fans in the stadium behind them."
The clubs have been in dispute since the match on 1 November was called off at half-time with the pitch waterlogged.
Ibrox chief executive Martin Bain has been critical of United, arguing that Rangers fans with ticket stubs from the original match should be entitled to free entry.
With the visitors likely to have around a quarter of their usual travelling support, Levein said: "It's a great thing that our fans will outnumber the Rangers supporters.
"It's maybe not the best news financially, but from the playing side it's good.
"It's not very often that you will be able to play the Old Firm and outnumber their supporters by five or six to one.
"I'd urge every United fan who can make it to come along and support the team."