FDP is CDU's preferred coalition partners both in Hesse and at the national level. But on national level, the CDU have instead been bound in an uneasy coalition with the Social Democrats (SPD) since 2005.
SPD were the big losers in the vote as their support in Hesse fell to 23.5 per cent from 36.7 percent, the exit polls showed.
In September, Merkel will battle Frank-Walter Steinmeier, the SPD foreign minister, for the post of chancellor.
Four other states will vote in the run-up to the federal poll.
As the German economy is facing its deepest recession since World War II, economic issues are expected to dominate the campaigns.
If, as expected, the CDU and FDP form a coalition in Hesse, five of Germany's biggest states containing over two-thirds of its population, will be ruled by regional CDU-FDP alliances.
This will boost hopes in Merkel's camp that a similar a centre-right alliance may be possible at national level after September's vote, instead of another coalition with the SPD.