The Veltins-Arena outfit currently lie fifth in the German top flight, with Wolfsburg the closest contenders to champions and runaway leaders Bayern Munich this season.
While Schalke have regularly been at the top end of the Bundesliga in recent seasons, local rivals Borussia Dortmund have generally offered more of a challenge to the Bavarian giants in that time.
Schalke have not won the German title since 1958 and with Dortmund struggling in 17th this term, Tonnies feels the club need to improve off the field to facilitate a title challenge in the near future.
"Money scores goals. If you want to challenge for a top three or four finish in the Bundesliga, then you've got to have a big budget," he told Sport Bild.
"We - the ones in charge - have got to ensure we can do that.
"I would like to see our membership levels rise from 130,000 to 200,000.
"We've got around 10 million fans and people who like us and with them, we have a big chance of continuing to grow as a club."
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