West Ham have asked Sunderland at what price they will sell striker Jermain Defoe, Sky sources understand.
Sky Sports News HQ reported earlier on Wednesday that the Hammers had been rebuffed in a £6m offer for the 34-year-old.
But it is understood they will test Sunderland's resolve by going back in with an increased offer.
Hammers boss Slaven Bilic is keen to add a striker to his squad in January with midfielder Michail Antonio their leading Premier League scorer by some distance on eight goals.
Hopes that Simone Zaza would provide goals to boost West Ham proved wide of the mark, with the Italy international appearing to be on his way out of the club in January.
Andre Ayew and Andy Carroll have both struggled with injury, combining for only three goals, leaving the Hammers scoring at only just over a goal a game.
Sunderland have struggled even more in front of goal with Defoe providing 11 of their 19 goals in the Premier League, including two penalties against Liverpool last time out.
Defoe started his professional career with West Ham and scored 41 goals before leaving for Tottenham in February 2004.