BERLIN (Reuters) - German engineering group Siemens has already attracted demand for all of the shares on offer in the initial public offering of its medical imaging and diagnostics business, one of the bookrunners leading the transaction said on Tuesday.

Siemens announced plans to float Healthineers on the Frankfurt stock exchange two weeks ago, putting it on track for a listing in late March in what would be one of Germany's biggest listings in recent years.

The offer period is expected to run from March 6-15. Siemens set the price range for the offering on Sunday, valuing the division at a smaller than expected 31 billion euros ($38.46 billion).

($1 = 0.8060 euros)

(Reporting by Arno Schuetze, writing by Emma Thomasson)