The Magpies made the bid earlier on Wednesday, but it has now been turned down by their Premier League rivals.
The add-ons were understood to be worth up to a further £5m which could take the total to £40m. Newcastle had a £25m bid rejected by the Bees for Wissa earlier this summer.
Wissa was absent for Brentford’s opening weekend fixture – a 3-1 defeat to Nottingham Forest – with Keith Andrews confirming his absence was linked to the speculation around the forward’s future.
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The west Londoners have already lost Bryan Mbeumo to Manchester United for £71m, captain Christian Norgaard to Arsenal and former head coach Thomas Frank moved to Spurs.
The 28-year-old was, however, seen in Brentford training on Tuesday. The Bees’ next fixture is a home game against Aston Villa on Saturday at 3pm.
The pursuit for Wissa comes after more uncertainty regarding Alexander Isak‘s future.
The Newcastle forward put out an explosive statement on Tuesday night regarding his transfer stand-off – saying his future with the Magpies “cannot continue” over “broken promises” made by the club.
This is after Liverpool saw a £110m bid rejected by Newcastle earlier this summer.
Isak has not yet featured for Eddie Howe’s side in matches since Newcastle returned to pre-season duty. He has been spotted at the club’s training ground and arrived just after 3pm on Wednesday to continue this training away from the first team.
The Magpies do not expect Isak to be sold this summer and say he will be welcome back to the fold whenever he is ready.
Sky Sports to show 215 live Premier League games this season
This season, Sky Sports’ Premier League coverage will increase from 128 matches to at least 215 games exclusively live.
And 80 per cent of all televised Premier League games this season will be on Sky Sports.
