Manchester City have set a £25 million price ceiling to land Aston Villa midfielder James Milner.
The Sunday Mirror says City, who had a £20m offer for the midfielder rejected before England flew out to South Africa, will test the Midlands club's resolve again when the tournament ends.
But City's football administrator Brian Marwood is unlikely to go higher if Villa show more reluctance to do business.
A City insider said: "It's been a frustrating time, but the owner, chairman and chief executive are adamant that they will not pay over-inflated prices."
"The fact we aren't in the Champions League has had a huge affect on plans, but so to has the determination to get good value."