West Ham have failed with an improved bid of £20m for Marko Arnautovic, according to Sky sources.
The offer is £5m more than a first Hammers bid, rejected by Stoke on Monday after Arnautovic handed in a transfer request, and has again been turned down.
Stoke are not looking to sell Arnautovic, who has been at the club for four years and signed a new contract last summer.
The Austria forward is on City's tour of Switzerland, where he suffered a suspected knee injury during Tuesday's friendly against Neuchatel Xamax.