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The match was postponed on Tuesday after snow made the pitch unplayable.
"You have to think whether or not it could all happen again here. It can all go wrong again in two weeks," Watzke told the news agency.
The Dortmund team bus had to be pulled out of mud by a tractor at Lotte.
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The Frimo Stadium holds just 10,059 fans and the team were playing in Germany's regional leagues before being promoted last season. They have beaten top-flight sides Werder Bremen and Bayer Leverkusen en route to the last eight.
The game may be replayed on Tuesday, 14 March, between Dortmund's Bundesliga matches against Hertha Berlin (11 March) and Ingolstadt (17 March).
Borussia Dortmund chief executive Hans-Joachim Watzke wants their German Cup quarter-final at third-tier Sportfeude Lotte moved away from the minnows' home ground, according to AFP.