Yes, your description fits the Haenel Schonzeitbüchse = off season/ varmint rifle model 1909. This model was indeed made in .25 Remington, though Haenel called it 25/35 randlos = rimless. The .25-35 aka 6.5x52R was well known in Germany, while "Remington" was most associated with outmoded blackpowder single shots and cheap plinking actions. DWM up to the 1930s offered both cartrridges with the same loads: 6.5x52R aka .25-35 Win, DWM case number 519, and 6.5x52 aka .25 Rem, case number 519A. Here is a scan from the 1909 Haenel catalog.

Translation:
Page 11, VII Closed season repeating rifles = "closed-season rifle" = Varmint/small game rifles
six shots,for Winchester-cartridges 25/35 rimless.Action and Magazine like

Haenel model 1909 System.
Magazine can be hand filled from top or bottom.
Sch.R.Nr. 1:Sch.R.Nr.1 Repeating stalking rifle system Haenel model 1909. Bolt with gas shield, bolt handle bent down and flat, barrel of modern steel by the Krupp steelworks, rear octagonal and round from foreend tip, integral rib on top, with long silver bead frontsight inserted from the front into the rib, standing rear sight with folding leaf; with good set trigger; sighting plane matted; walnut halfstock with cheekpiece and checkered pistolgrip; sling swivels; all parts case hardened and bolt pickled grey; for Winchester cartridge Cal. 25/35 rimless………….Mark 135.- each.
Length overall 104 cm = 41", weight 2.9 kg = 6.4 pounds.
Sch.R,Nr. 2: Same, but full stock with divided foreend to avoid tension on barrel, horn foreend tip Mk. 145.-
Optional on all rifles: Fold down peepsight , drift adjustable Mk. 7.50, screw adj. Mk. 10.- more
Cartridge magazine in buttstock with hinged lid: simple Mk6.-, better 10.-

These Haenel Schonzeitbüchsen are the rarest of the rare Haenel m 1900 and 1909 rifles. The rifle was merely retailed by Otto Bock. As the scope is light alloy, it was mounted later, post-1935.