In a short statement, Deutsche Bahn said discussions were ongoing but there could be no certainty an offer would be made.
Shares in Arriva were up 2.5 percent to 693.5 pence at 1040 GMT, building on a gain of 17 percent on Wednesday as traders cited market talk of a 700 pence-per-share bid.
A bid at this level would value Arriva at 1.2 billion pounds ($1.8 billion).
Arriva runs buses, rail franchises and other services in 12 European countries, making it one of the continent’s few public-transport operators with a wide international footprint.
Arriva's rivals include France's Keolis, and the firm that is being created by the merger of Veolia VIE.PA's Veolia Transport and Transdev, which is owned by state bank Caisse des Depots, as well as UK-focused First Group FGP.L and National Express NEX.L.
Arriva two weeks ago ended early-stage talks with SNCF SNCF.UL, the French state railway group over an equity tie-up with Keolis.
Earlier this month Arriva said 2009 pretax profit fell 19 percent to 121.7 million pounds.
(Reporting by Matt Scuffham; Editing by Victoria Bryan)
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