Newcastle’s bid is understood to have been £35m up-front and a further £5m in add-ons, a significant improvement on the £25m offer made earlier this summer.
But the fresh offer was quickly knocked back by Brentford, with one new report claiming the Bees have not provided an asking price to any team.
Newcastle will now go back to the drawing board and must quickly decide on whether to return to Brentford with another improved offer or turn their attention elsewhere as they continue their efforts to strengthen their forward line.
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Wissa wants the Newcastle move and didn’t feature for Brentford throughout pre-season or in their Premier League opener at Nottingham Forest on Sunday.
After the defeat at the City Ground, boss Keith Andrews admitted he wants the matter resolved “sooner rather than later”.
Wissa has been a leading target for Newcastle since early in the summer, with the Magpies’ pursuit of the 28-year-old unrelated to Alexander Isak’s situation.
Wissa was instead identified as a replacement for Callum Wilson, who left the club at the end of his contract and went on to join West Ham United.
Having made known his desire to leave, Wissa deleted all references to Brentford on his Instagram account.
The Bees completed the club-record signing of Dango Ouattara over the weekend, with Newcastle hoping that deal and their improved offer would spark progress in their pursuit of Wissa, but that hasn’t proved to be the case.