Imagine you're at a party and you see someone attractive, but no matter how hard you try, you can't make eye contact. Do you move on or does their apparent aloofness heighten your desire to make a connection?

It's a common paradox that the more eager you are to sell something, the less attractive it will be to the buyer. Think about your day-to-day life. When you hear that a show you want to see is sold out, what happens to your desire to get a ticket?

You face the same challenge when you decide you want to sell your company: The more you look eager to sell your business, the less likely you are to get an offer. We recently analyzed nearly 10,000 businesses that have used our tool at The Sellability Score, and we discovered that the longer you say you want to hang on to your business, the more likely you are to get an offer.

The contrast is stark. We asked business owners if they had received an acquisition offer in the last year. Then we asked them how long they expect to keep their business before selling it. Overall, 16.1 percent of the businesses we analyzed had received an acquisition offer in the last year. For those planning to get out within the next two years, 14.6% had received on offer, meaning the folks who want to get out sooner are a little less likely to get an offer.

For those with a two- to five-year time horizon for getting out, 16.2 percent had received an offer. But for those businesses whose owners say they plan to keep the business for 20 or more years (the longest time horizon we measure), the likelihood that they had received an offer jumped to 45.6 percent--almost three times higher than average.

It's natural for your business to be more desirable the less you appear to want to sell it, but what do you do if you're keen to get an offer but don't want to appear desperate? Here are three suggestions for getting an offer without asking for one:

1. Become an industry darling

Acquirers usually shop for companies in their own industry, so they often track the industry-specific media and attend industry events. That's why it's useful to hire a PR professional to get you some media attention in your industry. The good news is that while a cover story in The New York Times is hard to come by, getting the attention of an editor or producer at your industry-specific media outlet is a lot easier. While industry-specific media won't move the sales needle as quickly, it may well garner you the attention of a potential acquirer.

2. Grab a seat on the board

Unpaid board work may sound like boring bureaucracy; all those consensus-building meetings can seem like a time suck for a hard-charging business owner. But being an active member of your industry association board will bring you and your company to the attention of the acquirers in your industry without you having to say you're for sale.

3. Strut your stuff on stage

Industry awards ceremonies can seem like self-congratulatory nonsense. After all, nobody outside your industry cares that you've won the widget maker of the year award three years in a row--except, of course, the bigger companies in your field who will watch with interest (and perhaps a modicum of envy) as you strut across the stage to accept your award.

In short, looking desperate to sell is a surefire way to minimize your appeal to a buyer. Instead, become an industry star and acquirers will find you all on their own.