Arsenal are prepared to go higher after making an opening offer for West Ham captain Declan Rice.
Sky Deutschland says Bayern Munich intermediaries have learned that Arsenal have offered 70m for the midfielder.
However with Bayern also keen, West Ham are seeking 100m to part with their captain - either in straight cash or with players to make up the difference.
Bayern are yet to make their proposal, though coach Thomas Tuchel is insisting they compete for Rice's signature. The German has spoken directly to the midfielder over the phone.
Arsenal's current richest signing is Nicolas Pepe at 72m.