What: Shares of touchscreen controller specialist Synaptics (NASDAQ:SYNA) enjoyed a good September, with shares jumping 18%. What's particularly impressive about the move is that Synaptics had lost 8% of its value up until the very last trading day when shares soared 27% on reports that the company rejected a takeover bid.

So what: On the final day of September, Bloomberg reported that a state-backed investment group in China had made an offer for Synaptics, valuing the company at nearly $4 billion, or $110 per share. That price represented an incredible 70% premium compared to the prior day's close, but evidently it still wasn't enough to convince Synaptics to sell. The company would be more open to considering a $125 per share offer a little more tenable, according to the report.

Now what: Synaptics has benefited from the rise of mobile devices, as it supplies critical components that make touch-based input possible in modern gadgets from the world's top vendors of smartphones, tablets, and computers. Mobile products accounted for 89% of revenue last quarter. Chinese entities have been making numerous offers in recent times to scoop up semiconductor companies with the hopes of vertically integrating technologies within The Middle Kingdom, and several deals have already gone through this year.

More recently, Synaptics has introduced a new set of touchscreen controllers that can facilitate pressure sensitive interactions, much like the 3D Touch feature found in the new iPhone 6s. It's inevitable that this functionality will find its way into the Android camp, and Synaptics is well positioned as the supplier to make that happen, and considering the geographical concentration of smartphone OEMs, it's no wonder that Chinese companies are interested in acquiring Synaptics.

Of course, the fact that Synaptics has supposedly rejected a $110 per share bid strongly suggests that the company believes it is worth far more than that. Either way, with shares currently trading in the neighborhood of $84, a lot of potential upside remains if the company is indeed entertaining buyout offers at all. 

Evan Niu, CFA has no position in any stocks mentioned. The Motley Fool has no position in any of the stocks mentioned. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.